In a defeat for President Carter, the Senate bowed to a Republican filibuster yesterday and killed public financing for Senate elections, 36 to 39.

The public financing provisions for which the President made a strong plea at his press conference only a week ago, were stripped from a campaign, law bill after the Senate for the third successive time, failed by a wide margin to cut off a filibuster engineered by minority leader Howard H. Baker Jr. (R-Tenn.) and backed by a coalition of conservative organizations.

With 60 votes needed to limit debate supporters of public financing won a majority of only 52 to 46 yesterday, eight votes short. The vote showed that the filibuster could not be broken, and supporters of public financing. Including sponsor Dick Clark (D-Iowa), majority Leader Robert C. Byrd (D.W. Va.) and whip Alan Cranston (D. Calif) then agreed to strike out public financing and pass what little remained of the bill.

Baker contending the public financing and pass what little remained of the bill.

Baker contending the public financing provisions would help Democrats far more than Republicans in elections, applied heavy party-unity pressure on Republicans to vote against debate-limiting cloture.

At the same time many Southern Democrats, some of whom are now elected over poorly financed, token GOP opposition but would face well-financed Republican opponents under public financing, bolted Democratic ranks and voted to keep the filibuster alive. In all three cloture votes, at least 10 Southern Democrats voted with Republicans.

Defeat of public financing signals extreme difficulties for the remaining three items in Carter's political package, none of which has yet reached the Senate floor. They are voter registration, direct election of the President and reision of the Hatch Act. Public financing advocates had estimated that of the four bills, it had the best chance of beating a filibuster.

Under the financing bill, candidates of a major party in Senate election races (primaries were not covered) could have received up to 62.3 per cent of their campaign costs from the Treasury, provided they accepted an overall spending limit based on state voting-age population. Sponsors estimated the cost for the 1978 Senate elections at $14 million to $18 million. They said he bill would free candidates of obligations to special-interest groups that normally finance campaigns.

Common Cause, a citizen's lobby ardently backing the financing bill, said after it was killed yesterday: "Senate Republicans have made it abundantly clear that the privileges of the rich and the influence of powerful economic interests reign supreme in the Republican Party."

A coalition of conservative groups, including the American Conservative Union, National Conservative Political Action Committee. Committee for Survival of Free Congress. Young Americans for Freedom and the Chamber of Commerce carried on a strong lobbying and grass-roots campaign against public financing, an ACU spokesman said yesterday.