DES MOINES, FEB. 8 -- Sen. Robert J. Dole (R-Kan.) tonight won an easy victory in the Iowa precinct caucuses, and television evangelist Pat Robertson stormed past Vice President Bush for second place in the first test of the race for the Republican presidential nomination.

The results were a stunning blow to Bush in the state that first propelled him into national prominence eight years ago, and will put him into a fight for political survival as the race moves to New Hampshire next week.

Robertson's strong second-place finish, built on mobilizing evangelical Christians on moral issues, establishes him as a major player in the race.

With 98 percent of precincts reporting, Dole had 37 percent of the vote, Robertson 25 percent, and Bush 19 percent. Bush, who had maintained what was thought to be an effective political organization in the state for nine years, received fewer than 20,000 votes, about 13,000 less than he received here eight years ago. There were 37 Republican delegates at stake.

Rep. Jack Kemp (R-N.Y.), who had hoped for a third-place finish, was fourth with 11 percent followed by former Delaware governor Pierre S. (Pete) du Pont IV with 7 percent. Former secretary of state Alexander M. Haig Jr., who campaigned little in Iowa, received less than 1 percent of the votes.

Robertson was overjoyed with his showing. "It is a victory for those who want Americans to be No. 1 in the world, and want to restore the greatness of America through moral strength," he told cheering supporters here.

"This is the test I had looked for to see if the base that supports me could indeed be broadened, and I think the voters of Iowa have given accent to this. I'm going to be reaching out to all Americans. I don't want to be a candidate of some narrow sphere of interest."

Dole said he was "surprised" by Bush's poor finish. "We feel talking about the issues paid off," he said in one television interview. "The people of Iowa decided Bob Dole can make a difference," he said.

William E. Brock, Dole's national campaign chairman, said Bush "has taken a direct hit" that will be hard to recover from. "It is a disaster for Bush," he said. "I think they'll be scrambling with everything they've got to hang on by their fingernails."

Richard Wirthlin, Dole's pollster, said "there's no question this will narrow the gap between George Bush and Bob Dole. It is not the end of George Bush, but the race is much more close."

Bush forces here looked stunned as they congratulated the victors. "What happened is we got whipped in Iowa," said George Bush Jr., the vice president's oldest son. Rich Bond, Bush's deputy campaign manager, said the defeat "wasn't a big surprise" and "we were ready for it."

"All I can tell you is it was a lot more fun in 1980," said Bond, who directed Bush's 1980 campaign here.

Bush, who had left Iowa at midday for New Hampshire, conceded defeat at a news conference in Nashua, N.H., and said he was "disappointed" by the Iowa outcome. He vowed to try to "get the message out better" in New Hampshire.

But the vice president said he would do "nothing different on the message itself."

Bush said he saw "no evidence" in polls that lingering questions about the Iran-contra scandal hurt his Iowa campaign over the last five weeks and said he does not think his defeat was a repudiation of President Reagan.

He said Robertson had "out-hustled us" and offered congratulations to Robertson and Dole, adding he would be "coming after 'em."

"Iowa is behind us," Bush Jr. said. "Round one is over. Round two starts tommorrow when George Bush wakes up in New Hampshire. Don't count him out. He's a winner."

Robertson finished almost twice as strongly as the most optimistic pre-caucus polls predicted, and his showing was a tribute to the strength of the "invisible army" he mobilized in this moderate state over the last two years.

Robertson hailed his second-place finish as "a smashing victory," and predicted the showing would "put a rocket engine" into his drive for the nomination.

"It makes Pat Robertson a credible candidate," said Richard Pinsky, Robertson's national political director. "People have always liked what Pat Robertson has been saying, but now people are seeing he can win. I think we'll see movement conservatives rallying around him.

The GOP race, in its closing days, was dominated by an acrimonious battle between Bush and Dole, the two seasoned front-runners, as quiet hints of Robertson's strength became more evident.

As Republicans went to caucuses, both campaigns had worried about the major wild card in the race -- Robertson -- and his "invisible army."

Robertson, a political newcomer, had shocked Bush and the party establishment last September when he won a straw poll at a statewide party fund-raiser, and he has been considered a force to be dealt with ever since.

A Des Moines Register poll, conducted Jan. 25 to Feb. 5, found Robertson, who has never held elective office, virtually tied for second place with the vice president among those who said they definitely planned to attend the caucuses. Dole led both by 15 percent.

Almost forgotten in the results was the final, nasty battle between the two front-runners that had begun when George Wittgraf, Bush's Iowa chairman, issued a news release that raised questions about a no-bid, $30 million government contract awarded a former Dole aide.

Wittgraf accused Dole of a "record of cronyism" and a "history of mean-spiritedness" that "nearly single-handedly brought the Republican national ticket down to defeat" in 1976.

Dole reacted angrily, shaking the news release in Bush's face and demanding an apology from him on the floor of the U.S. Senate.

The exchange, which continued into the weekend, disgusted many Republicans. "I think a flap like this hurts both candidates in Iowa. We like positive politics here," said Sen. Charles E. Grassley (R-Iowa), a Dole supporter. "I think it could cost each of them about 3 percent caucus night."

It was the Iowa caucuses that first propelled Bush, then an obscure former Texas congressman, into national prominence in 1980. He upset Ronald Reagan, who had begun his career as a radio announcer in Des Moines, 32 percent to 29 percent. Dole finished seventh, with only 1 percent of the vote.

Dole frequently used his poor showing eight years ago to debunk claims by Bush forces this year that Iowa is a "quasi-home state" for him. "I was a neighbor then," the Kansas senator told crowds. "Nobody seemed to notice, and I finished dead last."

A strong showing in Iowa was considered critical for Dole's chances for the nomination because he is a Midwesterner and has not established as strong a political base elsewhere as the vice president.

Dole campaigned in Iowa 51 days, and his wife, Elizabeth Hanford Dole, the former secretary of transportation, visited 91 of the state's 99 counties. Bush campaigned here 38 days, 10 more than he did in 1980, and dispatched his deputy campaign manager, Rich Bond, to oversee Iowa operations after the Robertson straw poll victory last September.

Dole was portrayed as a strong leader who is "one of us." "I'm from Kansas. We're all Midwesterners. I grew up in a small town, and understand small-town values," he said again and again.

Grassley's endorsement was also important. One woman, for example, stood up at a town meeting in Glenwood, Iowa, Sunday and told Dole she did not know much about him, but "I've known Chuck Grassley a long time. He's been in my house and I've been in his. If he supports you, I have to know you're pretty good."

Bush, largely by virtue of his victory here eight years ago and the political organization he had maintained here ever since, was considered the early Iowa front-runner.

But his campaign was plagued by early organizational problems and overconfidence, by the state's long-depressed farm economy, nagging questions about his role in the Iran-contra scandals and a failure to establish an identity of his own apart from President Reagan, who is less popular here than elsewhere in the country.

Dole had held a small but steady lead in polls since last summer. By earlier last fall, he had built an effective political organization under Tom Synhorst, a former Grassley aide.

Robertson began building a base of support almost two years ago among evangelical Christians and viewers of his "700 Club" television program on his Christian Broadcasting Network.

The Republican establishment initially gave his efforts little chance of success. But they began taking Robertson seriously last fall after his straw poll victory, and all the other Republican contenders began courting evangelical voters.

But it became clear that Robertson had created an unusually dedicated corps of supporters when he made two whistle-stop bus tours across the state in the closing weeks of the campaign.

Dole forces, although they spent much of last week trying to play down their chances here, were prepared for a clear victory. While most caucuses were still in session, the campaign distributed a mimeographed "Post-Caucus Analysis" offering the campaign's account of "Why Dole Won" and "Why Bush Lost."

The analysis attributed the Dole win to a belief among Iowans that Dole is a "strong leader," he "can make a real difference," and that he shares the same values as Iowans.

It blames Bush's loss on doubts about his "leadership strength, nagging questions about the Iran-contra scandal and the fact that "caucus-goers -- and primary voters, too -- work for a living and want a president who has faced similar problems."

Republicans declare their presidential preferences in a secret straw vote held at the start of each caucus. The results are then phoned in to the News Election Service, a vote-gathering service financed by news organizations.

The caucus turnout appeared to be about the same as in 1980, when 110,000 attended, despite the fact that Robertson brought thousands of former Democrats and new participants into the process. This indicates a failure on the part of the Bush organization, in particular, to draw its supporters to the caucuses, and perhaps a falloff of interest among traditional Republicans.