Before a gallery studded with luminaries of the U.S. civil rights movement and the leaders of the District of Columbia government, the Senate last night approved by a one-vote margin a historic constitutional amendment that would give District residents voting representation in Congress.

The breath-taking roll call vote was 67 to 32 - one more than the required two-thirds majority - and came after several days of intensive lobbying by both sides.

Depsite a call before the vote by Vice President Mondale for quiet afterward, supporters of the amendment did not restrain their joy. The applause was led by Mayor Walter E. Washington in the gallery, and on the Senate floor by D.C. Del. Walter E. Fauntroy with hugs and handshakes, beginning with Sen. Edward M. Kennedy (D-Mass.), the legislation's floor leader.

The House approved the legislation last spring. Still ahead is the potentially difficult process of obtaining ratification by at least 38 state legislatures within the next seven years.

Although ratification is by no means certain, the same coalition of senators and citizens that guided the bill through the Congress pledged last night to push for an early vote by the respective state legislatures.

If it is ratified by the states, the question of whether the city would get one or two seats in the House would be determined on the basis of the 1980 census. The House membership has remained at 435 as additional states have been admitted to the union. The Senate, however, would be expanded to 102 members to accomodate the District's senators if the constitutional amendment is ratified.

After last night's vote, supporters jammed the hallways outside th Senate chamber, and dignitaries swarmed into the reception room where the vice president pounded the shoulders of Clarence Mitchell of the NAACP. Coretta Scott King, widow of the Rev. Martin Luther King Jr., was embraced by several senators.

The outcome of the vote, called in alphabetical order, was in doubt to the end. After 60 senatros had voted, the tally was 40 to 20, and at the end of the first full round, it was 60 to 29. Some known supporters, including Senate Majority Leader Robert C. Byrd (D-W. Va.) and republicans Robert Dole of Kansas, Barry Goldwater of Arizona and Charles Percy of Illinois, had held back their "aye" votes momentarily.

Sen. Orrin G. Hatch (R-Utah), one of the more outspoken foes of the proposal, shook hands with Dick Clark of Common Cause and said "Sorry I had to fight you," explaining that he opposed the amendment because he believed it was unconstitutional.

It was a similar statement by Hatch on the Senate floor just before the vote that prompted Majority Leader Byrd to scold Hatch, in a lecturing tone of voice, that "the Constitution is a living document. A constitutional amendment can't be unconstitutional. That is a fatal flaw in the argument of those who make that very curious objection."

After the vote, both Kennedy and Fauntroy praised the bipartisan support that the bill had received and credited the strong support of Republicans and Democrats with the amendment's passage.

But both of them and city leaders said the vote was just a first step because the state legislatures must now be faced.

"Strong bipartisan support was able to raise what is a fundamental issue of justice and equality," Kennedy said, "that people who have fought in our wars and have a population greater than that of seven other states ought to have voting representation in the Congress of the United States."

"We put together a masterpiece of strategy and timing that made this day possible," Fauntroy said.

He said a network of black-officials, including Gary, Ind., Mayor Richard Hatcher, Urban League Executive Director Vernon Jordan, Southern Christian Leadership Conference President Dr. Joseph Lowery, Mrs. King and Martin Luther King Sr. had been extremely helpful in gathering votes for the amendment.