The Republican-controlled Senate Budget Committee cut loose from President Reagan yesterday and voted, 13 to 4, to give the Democrats a surprising, if temporary, victory in approving an $849 billion budget for next fiscal year that would raise taxes by $30 billion, enough to jeopardize Reagan's tax-cut program.

Stymied by bitter divisions in GOP ranks, Committee Chairman Pete V. Domenici (R-N.M.) and three other Republicans turned to the Democrats to break a stubborn deadlock on taxes by, in effect, swallowing whole the Democrats' plan for tax increases in fiscal 1984.

But Domenici promptly served notice that the Republicans' vote was only an expedient to get a budget to the Senate floor, and volunteered to lead the fight there to junk the Democrats' $30 billion in tax increases in favor of Reagan's plan to hold off any major tax increases until fiscal 1986 at the earliest.

He also said he would join Reagan in seeking more money than the Budget Committee recommended in its resolution for defense, but indicated that he would not fight for the domestic spending cuts the president wants.

Changes in the tax and defense figures, for bargaining purposes if nothing else, are considered likely when the Senate takes up the budget in about 10 days. The House has approved a fiscal 1984 budget resolution with a $30 billion tax increase, along with less defense and more social welfare spending than the Senate committee approved. At the White House, spokesman Larry Speakes said it would be a "gross disservice to the American people" if the committee's plan prevailed but added that the administration thinks it has a "better chance" of winning on the Senate floor than it did in committee.

"Speechless. Strong letter to follow," said Sen. Robert J. Dole (R-Kan.), whose Finance Committee would have to enact the new taxes.

In addition to defying Reagan on taxes, the Senate committee approved only half his proposed 10 percent after-inflation increase in spending for the Pentagon and refused to go along with $11 billion in domestic spending cuts that Reagan had proposed for next year.

It also spurned a last-minute request from the White House for a one-day delay to work on rebellious Republican conservatives. The conservatives scuttled a proffered Reagan compromise Wednesday because of objections to the president's tax program, which would hold the line on taxes through 1985 but provide for $150 billion in "standby" tax increases starting in 1986. While the Democrats think his tax proposals are too low, these Republicans regard them as too high.

"I couldn't wait any longer . . . . I made a decision there was little chance of getting a solid Republican budget resolution. I think I was right," Domenici said.

On the crucial vote on taxes, the committee approved the Democratic plan, 12 to 4, with Republicans Nancy Landon Kassebaum (Kan.), Mark Andrews (N.D.) and Slade Gorton (Wash.) joining Domenici in voting with eight committee Democrats. Republicans William L. Armstrong (Colo.), Rudy Boschwitz (Minn.), Charles E. Grassley (Iowa) and Dan Quayle (Ind.) voted no.

On 13-to-4 passage of the budget resolution, only five Republicans--Domenici, Kassebaum, Boschwitz, Andrews and Gorton--voted yes. This was two votes short of a majority of all Republicans on the committee, which the Senate Republican leadership was depending on to avert the impression of a "Democratic budget." Voting against the budget were Armstrong, Grassley, Quayle and Ernest F. Hollings (D-S.C.), who has championed a budget freeze.

The committee-approved budget anticipates a fiscal 1984 deficit of $162 billion, which is roughly $30 billion less than a congressional re-estimate of Reagan's deficits because of the proposed tax increase.

Ranking committee Democrat Lawton Chiles (Fla.) told reporters after the vote that the scheduled 10 percent income tax cut scheduled for July 1 was not necessarily threatened by the budget, even though the $30 billion in proposed new taxes is precisely enough to accommodate repeal of the tax cut. With an income surtax, for instance, he said, "The president could keep his pride and the third year of his tax cut."

Domenici, however, said there is "no chance" that the Senate will approve $30 billion in new taxes for next fiscal year.

Domenici decided to abandon pursuit of a Republican budget and cut a deal with the Democrats after failure of the White House initiative and after consulting with both Majority Leader Howard H. Baker Jr. (R-Tenn.) and Sen. Paul Laxalt (R-Nev.), Reagan's closest friend in Congress. Neither were said to have tried to dissuade him, and Baker told Domenici he would back him in whatever he did, aides said.

Domenici, who worked closely with Chiles in trying to end the budget impasse that both feared might destroy the congressional budget control process, told Chiles over lunch what he was planning to do. Then in a caucus, Chiles lined up the Democrats.

Shortly before the committee was to vote, White House chief of staff James A. Baker III returned an earlier call from Domenici to tell him the White House was only a vote or two short of rounding up a Republican majority for a budget compromise. But at least one of the conservatives, Armstrong, remained adamant in his stand against a compromise, thereby dooming prospects for a Republican budget on the committee, which the Republicans control by only two votes.

"Once again, it was too little, too late," grumbled a GOP aide in an echo of what many Republicans have described as a major bungling of the budget by the White House this year after its big successes of 1981 and 1982.

Among the domestic spending increases the committee approved was a 4 percent pay increase for federal workers in April, a six-month delay instead of the pay freeze proposed by Reagan.