Proponents of a three-year extension of the deadline for ratifying the Equal Rights Amendment won a key victory yesterday in the Senate, apparently presaging an affirmative vote tomorrow on the extension proposal.

By 54 to 44, the Senate defeated an amendment by Sen. Jake Garn (R-Utah) that would have legitimized actions by state legislatures retracting ratification they had voted previously. Four state legislatures have voted, but the legality of these recisions is open to question.

Garn's amendment was intended to declare recision votes valid if taken during the three years from 1979 to 1982. Those are the extra years that the extension proposal would give the states to act on ERA. Proponents of ERA - a simple declaration that discrimination by sex is illegal - thought that any chance of ratification by the necessary 38 states would be doomed if the Garn amendment passed. Thirty-five states have ratified so far.

Proponents of ERA, led by Sen, Birch Bayh (D-Ind), made yesterday's vote a referendum on the constitutional amendment itself, arguing publicly and in intense private lobbying that a vote for the Garn proposal amounted to a vote to kill ERA.

President Carter and Vice President Mondale joined the lobbying calls to a handful of key undecided senators.

As of late Tuesday, pro-ERA lobbyists counted a dozen undecided, with the remainder split 46 to 42 against Garn's amendment. Ten of the 12 ended up voting against the proposal, a rush of pro-ERA sentiment that feminist Betty Friedan described last night as a "wonderful victory for the democratic process."

As Friedan and other pro-ERA activists acknowledged, lobbying was intense in recent days. Among the most effective lobbyists were the wives of undecided senators who prevailed on their spouses to vote against the Garn amendment. One of these was Susan DeConcini, wife of the freshman Democrat from Arizona.

National public Radio reported last night that senators' wives had played a role in persuading Majority Leader Robert C. Byrd (D-W, Va.) to bring the ERA extension to the floor during the hectic closing days of this session.

NPR correspondent Cokie Roberts said Senate wives Lori L. Riegle, Rita Hollings and Susan DeConcini, plus Sharon Percy Rockefeller, daugher of Sen. Charles H. Percy and wife of West Virginia Gov. John D. Rockefeller IV, helped persuade Byrd to bring up the bill. Jean Mondale also lobbied the majority leader. (Mrs. Hollings, however, could not persuade her husband, Sen. Srnest F. Hollings (D-S.C.) to vote against the Garn amendment.)

ERA backers also took credit for the decision to send Sen. Thomas F. Eagleton (D-Mo.) to Rome as a U.S. representative at the funeral of Pope John Paul I. Eagleton had announced his intention to vote for the Garn amendment.

An Air Force plane flew Sen. Floyd K. Haskell (D-Colo.) here from his home state Tuesday night so that he could cote against the amendment.

Sen. James B. Pearson (R-Kan) was at the United Nations and did not vote Backers of ERA said he had "taken a walk" to help them.

Bayh and Garn agreed yesterday that the basic ERA extension provision would pass easily tomorrow.

The same extension provision has passed the House. Among other effects, Garn's amendment would have forced a conference and and opponents felt they could have bottled up the legislation in committee until Congress adjourned. Thus ERA proponents had a double reason for resisting the Garn provision.

While 35 states have ratified ERA, backers have been unable to get three more states, so they turned to the idea of extending the seven-year deadline for ratification.

This decision alarmed some senators who were original supporters of ERA. One of them was Adlai E. Stevenson (D-IIL.) who spoke out against taking liberties with the constitutional process, even the behalf of a desirable amendment.

Garn said repeatedly during the debate that if the issue had been extending the deadline for ratification of a pro-abortion amendment, many who lobbied strongly for this extension would have opposed that one with equal vehemence.

Garn argued that a senator could vote for his amendment out of concern for sound constitutional principles and still support ERA, but he failed to win a majority. Other Senate conservatives who - like Garn - oppose ERA were split over the wisdom of his tactics, which involved voluntarily giving up the right to filibuster the ERA extension meansure in return for a scheduled up-or-down vote on his amendment.