Sen. Lowell P. Weicker Jr. won endorsement for a third term today from the Connecticut Republican convention, defeating Prescott S. Bush Jr., brother of Vice President Bush, by almost 2 to 1.

Weicker rolled up a 609-to-321-vote victory over Bush, but the challenger immediately said he would carry the fight into a Sept. 7 primary. "We're going to have the primary, no question about that," Bush said as the roll call ended and aides--some of them more hesitant about continuing the battle--hustled him off to a hotel suite to discuss the wisdom of a formal decision to carry on the contest.

The two millionaires, both raised in the wealthy New York City suburb of Greenwich, each collected and spent $1 million in the convention battle. Estimates are that the six-week primary campaign may cost them and their backers an additional half-million dollars apiece, before the winner faces Rep. Toby Moffett, the Democratic nominee, on Nov. 2.

Under Connecticut's "challenge primary" law, Bush had to win 20 percent of the vote today to force Weicker into a primary election. Polls have shown the incumbent's frequent dissents from Reagan administration policies and uninhibited flouting of party discipline might make him vulnerable to defeat in the primary.

The latest published poll, taken seven weeks ago, showed Bush with a 56-to-32 percent lead over Weicker among likely GOP primary voters. But Weicker is acknowledged even by Bush supporters to have gained strength since then, and Weicker claimed his private poll last week showed that, with the convention endorsement, he would be a 7-point favorite over Bush in the GOP primary.

In a shirtsleeves address accepting the convention endorsement tonight, Weicker said he had "no apologies" about the controversial stands that earlier this year threatened to drive him from the Republican Party to seek reelection as an independent. He said he would accept the Bush challenge "or anything that comes my way . . . from the illogic of extreme philosophy or the politics of ambitious opponents."

He told his many critics in the audience that he would "not ask you to stop grousing about Lowell Weicker--that would take the fun out of being a Republican in Connecticut." He promised that after "victory in November" he would continue "to use my power for the powerless."

The Senate roll call was unemotional because the delegates were exhausted by a dramatic, four-hour battle for the gubernatorial endorsement, which finally saw former state senator Lewis D. Rome edge state Sen. Richard C. Bozzuto after frantic and protracted vote-switching at the end of the first ballot.

Bozzuto, like Bush, has 10 days to decide if he will seek a primary. The winner will face Gov. William A. O'Neill (D).

But the torpor of the Senate roll call did not obliterate the high temper in the Weicker-Bush battle, the latest chapter in a continuing political feud between the two families.

The Bush forces papered the convention hall with reprints of newspaper stories quoting Weicker blasts at the economic and social policies of the Reagan-Bush administration and charged the incumbent with being a turncoat.

But Weicker won support from party leaders and rank-and-file delegates by portraying himself, as his sign said, as "Weicker the Winner." The senator has never lost an election and is the only Republican in statewide office today.

Weicker cited polls showing him running from 12 to 20 percentage points better than Bush against Moffett. But even in his own polls, Weicker faces a close race with Bush in a primary in which only the 440,000 enrolled Republicans can vote.

In the 1980 Senate primary, those voters nominated conservative James L. Buckley over the more moderate Bozzuto, and Buckley then went on to lose to Democrat Rep. Christopher J. Dodd.

Tom D'Amore, Weicker's manager, said the primary with Bush might cost the two candidates another $1 million, with another $500,000 possibly being spent by the National Conservative Political Action Committee (NCPAC), which is out to beat Weicker with its independent expenditures.

But there were also doubts about the fund-raising and political challenge on the Bush side, particularly in view of his showing in the convention today. A week ago, the Bush camp had hoped to top 40 percent of the vote, and as the balloting began, a key adviser said it would be difficult to mount a credible primary challenge with less than one-third of the convention votes.

Bush's 35 percent exactly matched the Weicker camp's estimate of his strength and was barely past the "credibility threshold."

The intensity of the Weicker-Bush battle was reflected in the nominating speeches, delivered after midnight Friday as the opening convention session came to its end. Hartford Councilman John O'Connell described Weicker as a politician of "confrontation and obstruction . . . who will tolerate no opinion other than his own . . . and who claims he will win by being a better Democrat than Toby Moffett."

But the pro-Bush rhetoric was mild compared to that used by Roger W. Eddy, treasurer of the state GOP, in nominating Weicker. He said the Bush campaign was powered by "a handful of men and women of the rigid right. A year ago, they lit their fire, and tomorrow they hope to smell burning flesh.

"Make no mistake about it, this is more than a Republican convention--it is a Republican trial. An inquisition. A few angry people have defined Republicanism in their own narrow, intolerant image, and whoever does not accept their definition as Republican gospel will, if they have their way, be burned at the political stake."