The House Democrats won their first big budget victory of the Reagan era yesterday with a carefully crafted tax-and-spending mix and a show of discipline from their freshman members rivaling that of the so-called "Reagan robots" of 1981.

They used the enhanced majority the voters gave them in November to beat an outnumbered Republican minority that was fighting with one hand tied behind its back, under White House instructions to offer no alternative of its own.

In the wake of the strongly partisan 229-to-196 vote for the Democratic budget resolution, the victors claimed they had demonstrated their readiness to govern and the losers said they had picked up an issue that will help them keep the White House in 1984.

"Everyone sensed that if we couldn't put it together today, we'd be right back in the minority status we had in 1981-82," said Rep. Leon E. Panetta (D-Calif.), a key member of the Budget Committee.

But Rep. Guy Vander Jagt (R-Mich.), chairman of the Republican Congressional Campaign Committee, said, "They've goofed. They have handed us a significant campaign issue with . . . their return to ever-increasing taxes and spending."

But those fears seemed far away as jubilant Democrats cheered the vote and pounded the back of Budget Committee Chairman James R. Jones (D-Okla.), savoring his first victory after a long string of defeats in his two years as head of the committee.

Democrats lost only 36 votes on the measure--three fewer than Jones said their advance count indicated they would--and gained four Republican crossovers.

Particularly impressive was the support from the newly elected Democrats who had been admonished by their leadership--still hurting from Democratic defections last year--that "every member of our caucus is expected to vote with our party" on the budget.

Fifty-two of the 58 freshmen voted with Jones in a showing that Majority Leader James C. Wright Jr. (D-Tex.) said "reaffirms the results of last November's election and gives substance to the hopes we had for constructing a working majority in the House."

The 26-seat gain the Democrats scored in the midterm election was the key to yesterday's win. In last year's House, had Republicans suffered only four defections and picked up 36 Democratic votes, they would have won by a 13-vote margin.

In a complete role reversal from 1981-82, when Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) and the Democrats were steamrollered time and again by a coalition of Republicans and conservative, mostly southern, Democrats, yesterday it was Minority Leader Robert H. Michel (R-Ill.) who was left complaining that the Democrats had pushed their fiscal plan through in a thoroughly partisan "autocratic process."

Some Republicans complained, however, that they were sent unarmed into battle by the White House, which declined its opportunity under the rules to insist on a vote on either the president's original budget or some Republican variant on it before the Jones version came up.

White House strategists, who had asserted after the November election that the president could still command a narrow majority in the House on certain key fiscal issues, took a calculated gamble that, as one put it, "Jones has gone too far left" in fashioning a budget that called for substantial tax increases, reduced defense outlays and higher domestic spending.

Last week the president intervened to halt work on an alternative budget in the Republican-controlled Senate, so the administration and its business allies could concentrate on defeating the Democratic version in the House.

Their thinking was that a Reagan victory in the House would enable him to pressure Senate Republicans into voting for a higher defense figure.

But aides to Senate Budget Committee Chairman Pete V. Domenici (R-N.M.) said after the House vote that he and his committee are still looking at a defense spending increase of 5 percent after inflation, barely more than the House version and less than half the increase the president has sought.

The absence of a Republican alternative enabled House Democrats to corral votes from many moderate and conservative Democrats who had backed the earlier Reagan-endorsed budgets.

Twenty-two of the 47 current House Democrats who had voted for the Gramm-Latta (Reagan) budget in 1981 voted for the Jones budget yesterday.

Many of them were southern "Boll Weevils," who disagreed with its tax and defense provisions but were persuaded that the final version of the budget that emerges from a Senate-House conference will be more to their liking.

At the same time, by shifting to a more traditional Democratic mix, Jones was able to pick up votes from about two dozen black, Hispanic and liberal Democrats who had refused to vote for his 1981 and 1982 budgets.

Rep. Parren J. Mitchell (D-Md.) said it was the first budget he had supported since 1977, because "It's the first time we've moved to restore some of our vital domestic programs instead of constantly cutting them."

Both conservatives and liberals said the elaborate effort the Democratic leadership made to have every member on that side of the aisle fill out a questionnaire showing his own budget preferences gave them a sense of participation in the process they had not had before.

While Rep. Barber B. Conable Jr. (R-N.Y.) complained that Republicans had been excluded from what he called "the first step in the longest Democratic presidential campaign in history," another Republican, Rep. Newt Gingrich (R-Ga.) said, "This year, the Democrats found their themes, and it's the Republicans who are unfocused. We didn't have an alternative because we really don't have an alternative."