David Stockman scored a striking personal triumph with the budget compromise reached between President Reagan and the Republican leadership in the Senate. For Stockman led the way in pushing the concessions made by Reagan on the one hand and by the Senate leaders on the other.

The accord could go through Congress without major change, easing this country's biggest problem and opening the way to a successful second term. Even if the bargain falls apart, which is more likely, the budget process has at least been saved from a crippling impasse.

Two elements make up the budget compromise. First there are cuts in domestic spending, including elimination of 17 different programs chiefly beneficial to the middle class. Among those scrapped entirely are such crowd-pleasers as federal aid to school districts "impacted" by defense spending, the Small Business Administration, the Job Corps, Amtrak and the Appalachian Regional Commission. Major cuts are also due in another 30 programs, including farm price supports, student aid and housing subsidies.

Budget directors stretching back 25 years have had some of those programs on their cut lists. Stockman not only pushed them past the objections of interested Cabinet members, he was way out front in selling the reductions to Congress. Indeed he was publicly scolded by leading figures in Congress, by the thunderers of the press and by the White House itself for the zeal he showed in arguing for reductions in such political sacred cows as farm subsidies.

But he stuck to his guns inside the administration and out. To a large degree he has had his way. Some 90 percent of the programs he wanted eliminated from the budget are scrapped in the Republican compromise. He emerges as the chief political strategist for the president's war on government spending.

The second set of concessions was made by the president and Defense Secretary Caspar Weinberger. During the 1984 campaign, Reagan vowed that he would "never stand for a reduction in Social Security benefits." Later he modified the language to say that he would accept reductions if "faced with an overwhelming bipartisan majority in both houses" of Congress. As it is, he accepts, without Democratic support, a cut in benefits more stringent than that proposed by Republicans on the Senate Budget Committee.

A rise of 6 percent in military spending was also proposed at first by the president and Weinberger. They rejected an offer of 3 percent growth that was proffered by Majority Leader Robert Dole right after the budget was announced. Only when the Senate Budget Committee, under Chairman Pete Domenici, voted for no real growth in military spending did Reagan and Weinberger accept the compromise that calls for 3 percent growth.

From the first, Stockman had been for restrictions on cost-of-living increases in Social Security, and a 3 percent real growth figure in defense spending. Nor should praise be lavished on Reagan and Weinberger for hanging tough and only giving way to the inevitable. Had the present compromise been accepted in February, it would have acquired enough momentum to zip through the Republican Senate and appear almost irresistible to a majority in the Democratic House.

There remains, as matters stand now, a slim chance the compromise will clear the Senate as a budget reconciliation resolution. The merits of the compromise bulk large. It would cut the federal deficit by $300 billion over the next three years, relieving the economy of its worst burden and opening the way to an appealing tax reform. Though the Democrats vow a fight on Social Security, the Senate rules favor the Republican leadership.

Resistance in the Democratic House will be even stronger, with Speaker Tip O'Neill rallying support for many of the programs that would be eliminated. But there is at least an outside chance to beat the speaker. For many conservative Democrats are going to vote in favor of deficit reduction, particularly if it opens the way to a tax reform that is more popular among House Democrats than Republicans.

Even if resistance changes the compromise beyond recognition, the mere breaking of the logjam represents an undoubted achievement. For the budget process is rolling again. The administration is now plainly on record as wanting to make a serious effort to reduce deficits. Thus the United States is in far stronger position to turn aside foreign complaints that finger the budget deficit as the root of all evil. This country now has a better case for urging the Japanese to open markets. Resisting European pressure for radical reform of the monetary system also comes more easily. The strictly economic part of the economic summit scheduled for Bonn in May -- and the other meetings leading up to it this month -- should be a piece of cake.

Only very rarely is it possible to single out an individual for credit in American government. The system is a maze that connects everything to everything else. But in the case of the budget compromise there is no doubt. Stockman is the central figure. He emerges from the latest fracas with a claim to be the foremost budget director in our history.