By a surprising vote of 82 to 9, the Senate yesterday confirmed the nomination of Leonard Woodcock to be the first U.S. ambassador to the People's Republic of China.

Carter administration officials and their allies in the Senate both interpreted the large affirmative vote as a victory for President Carter, indicating broad support for his decision to normalize relations with the Peking government.

Until yesterday, conservatives led by Sen. Jesse Helms (R-N.C.) had threatened to filibuster the Woodcock nomination as a protest of the suddenness of Carter's Peking decision and of the absence of strict security guarantees from China for Taiwan.

But the threat of a filibuster evaporated, apparently because so few senators had any enthusiasm for making a symbol of Woodcock's nomination. On the final roll call, only seven senators, including Helms, voted "no" in the protest Helms originally planned. The other two "no" votes protested that the timing of his confirmation was an indirect sign of support for -- or at least indifference to -- the Chinese invasion of Vietnam.

After yesterday's vote it appeared likely that the Senate will support compromise legislation on Taiwan worked out last week by Sen. Frank Church (D-Idaho), chairman of the Foreign Relations Committee. This legislation includes a statement of support for Taiwan's de facto independence and future security. The Carter administration said it was unnecessary, but grudgingly accepted it.

Church's Taiwan language was drafted to satisfy numerous senators -- perhaps a majority -- who expressed discomfort when the Carter administration didn't exact specific assurances from Peking about Taiwan's future as a condition of normalization. The Church language has been criticized as inadequate by a few senators, but endorsed by a bipartisan coalition that seems to embrace a clear majority.

Some staff aides speculated yesterday that Church's success in working out this language defused whatever sentiment had existed for holding up the Woodcock nomination as a protest.

Even Helms had kind words for Church's role in yesterday's debate, praising him for contributing "more than anyone else" to the Foreign Relations Committee's improvements in the administration's Taiwan legislation.

The debate itself was relatively brief and mild. Some of the strongest rhetoric came from Sens. Charles McC. (Mac) Mathias (R-Md.) and S.I. Hayakawa (R-Calif.), the two who voted against Woodcock's nomination on grounds that a confirmation vote now would look like support for China's invasion of Vietnam.

Said Mathias, "we should tell the Chinese clearly and forcefully that they cannot make war and expect our new relationship to prosper." He urged the Senate to hold up the nomination because approving it now "would send out another wrong signal to a very troubled region."

Hayakawa supported this view. "China seems to have assumed that we are an ally of theirs against Russia," he said. "We are pretending that this disruption of international order which the People's Republic of China has committed does not exist. We are intent on doing business as usual... it is not a fitting way for the United States to behave..."

Church and others responded that the outbreak of hostilities between China and Vietnam was actually an important reason why the United States needs an ambassador in China as soon as possible.

Under the original normalization agreement, the two countries planned to exchange ambassadors on March 1. Woodcock's confirmation yesterday may make it possible for him to reach Peking by then.

Helms reportedly met for more than an hour last Friday with Dan Tate, President Carter's chief Senate lobbyist, who apparently urged him not to filibuster the Woodcock nomination.

Many of the staunchest conservatives declined to join Helms yesterday. Among those who voted for Woodcock's nomination were Paul Laxalt (R-Nev.), Strom Thurmond (R-S.C.), Barry Goldwater (R-Ariz.) and Harry F. Byrd Jr. (Ind.-Va.). Both Paul Sarbanes (D-Md.) and John W. Warner (R-Va.) voted for Woodcock