Republican Rep. Paul S. Trible, a fervent disciple of Reagan administration economic policies, defeated Democratic Lt. Gov. Richard J. Davis yesterday to become Virginia's next U.S. senator.

With all but 1 percent of the vote counted, Trible maintained a solid 51-to-49-percent edge, leading Davis by 724,492 votes to 689,815.

Trible, a 35-year-old Newport News congressman who portrayed himself as the philosophical heir to the state's retiring independent Sen. Harry F. Byrd Jr., will assume the seat that has been held for the past 50 years by either Byrd or his father, Harry F. Byrd Sr.

A crowd of about 700 joyous Republicans jammed the ornate Virginia Room of the John Marshall Hotel in Richmond last night, waving banners and cheering enthusiastically as Trible, his wife, Rosemary, and their two young children entered the room. "The story of this election is that the people of Virginia have hope for tomorrow," he declared. "This is a victory of philosophy fashioned by countless Virginians -- Republicans, Democrats and independents alike -- that share an abiding commitment to conservative principles of government."

In the Washington suburbs, Republican Frank R. Wolf easily staved off a challenge by Democrat Ira M. Lechner and Republican incumbent Stanford E. Parris narrowly beat Democrat Herbert E. Harris. Elsewhere in the state, Democrats appeared to have picked up three GOP-held congressional seats, ousting longtime incumbents Robert Daniel and William Wampler and winning an open seat vacated by retiring Republican M. Caldwell Butler.

Trible's victory last night, coming after last year's Democratic sweep of statewide offices, was a resounding personal triumph. In his own 1st Congressional District, a normally Democratic area that incudes Newport News and eastern Virginia, Trible captured nearly 62 percent of the vote.

Huge Trible majorities in Tidewater, the staunchly conservative Richmond suburbs and the traditionally Republican strongholds in the mountainous west more than made up for Davis' strength in the Washington suburbs, where the Democrat won with 52 percent of the vote.

Davis last night described his defeat as a repudiation of his campaign message that the country needed a "change of course" in national economic policies. Appearing at a somber campaign headquarters in Richmond with his wife, Martha, and Gov. Charles S. Robb, the defeated candidate told his supporters that "We did all the things in a very short time that we intended to do.

"We focused on the principal issues in Virginia -- high interest rates, unemployment, housing, massive business failures. We articulated those issues with eloquence. It appears that eloquence fell somewhat on deaf ears."

Pressed by his supporters on his way out the door, Davis was asked why he thought he had lost. "I didn't get enough votes and I'm sorry," he said.

Exit polls conducted by NBC and ABC throughout the state yesterday suggested that Virginia's traditional conservatism and Ronald Reagan, who had campaigned for Trible, may have been key factors in the Trible victory. According to ABC's poll, Virginians approve of Reagan's presidency by a 56-to-44 percent margin compared with a 52-to-48-percent disapproval of Reagan nationwide.

Only a day earlier, Trible's candidacy received a last-minute boost from the Reagan administration, which announced the awarding of a $280.9 million contract to the Newport News Shipbuilding and Dry Dock Co., the largest private employer in the state. "What a way to end a campaign," Trible told reporters. "I am exhilarated."

The election ended a bruising four-month campaign that saw personal attacks and negative advertising overshadow most issues. The tone was set early on as Trible portrayed Davis as a "Ted Kennedy liberal" in the pocket of "big labor." Davis flailed away at Trible as a "do-nothing, press-release" congressman. Each candidate accused the other of waging campaigns filled with "lies" and "distortions."

As recently as six months ago, national Republican strategists had expected an easy victory in Virginia that would help them solidify control of the Senate. Trible, who started campaigning for Byrd's job nearly two years ago, was blessed with a huge headstart in fund-raising and organization.

The Democrats were in disarray. Black state Sen. L. Douglas Wilder of Richmond at one point threatened to bolt the party and mount an independent candidacy in protest over the candidate first picked by party leaders, conservative state legislator Owen Pickett from Virginia Beach.

After Pickett bowed out to avoid a party bloodbath, the Democrats turned to Davis. But the former Portsmouth mayor, the favorite of the party rank and file, was reluctant from the outset. Still in debt from his campaign for lieutenant governor last year, Davis was uncertain about his ability to raise the necessary funds. He first spurned the pleadings of party leaders that he run, and only agreed to do so after he was drafted by delegates to the party's Roanoke convention in June.

By the time post-convention campaign finance reports were filed in July, Trible had opened up an enormous 16-to-1 fund-raising advantage, raising $520,983 to Davis' $32,465.

Davis began to close the gap quickly. His media adviser, nationally prominent Democratic consultant Robert Squier, and James Carville, his campaign manager imported from Louisiana, devised a strategy that played up Davis' "experience" and maturity, and kept Trible on the defensive with a blizzard of attacks on his legislative record and campaign tactics.

Some Trible blunders played into their hands. In August, his campaign put out a memo suggesting that Davis staffers had conspired with labor union representatives at a New York meeting to skirt federal campaign reporting requirements. Davis staffers cried foul, insisting that no such meeting ever took place. When Trible refused to disavow the memo, he was hounded by questions and the flap dominated early coverage of the campaign.

Although Trible recovered, Davis' consultants stuck to their strategy. Davis ducked most opportunities for face-to-face debates, while his campaign unleashed a series of controversial negative radio ads that attempted to ridicule Trible for congressional absenteeism and legislative ineffectiveness.

Trible fought back by bringing in President Reagan for a Richmond rally, but the visit failed to produce the surge that Republicans had hoped for. As the campaign went into its final weeks, the polls showed the candidates locked in a virtual dead heat. By the final week, it appeared Trible would end up spending over $1.6 million, compared with Davis' projected $1.1 million.

Mostly, the campaign reflected a contrast in styles. Trible was a young, intense, and primly formal candidate whose tendency to repeat the same campaign slogans over and over again led some of his own staffers to joke about his "robotized" delivery.

The older, white-haired Davis was more relaxed on the stump, quick with one-liners and occasionally self-deprecating humor. He criticized Trible for "blind ambition." As for himself, Davis said, "If I were not to win, it would not be the end of the world for me."