President Reagan's proposal for a free-trade pact with Canada squeaked through the Senate Finance Committee on a 10-to-10 tie vote yesterday after the president persuaded one senator to switch his vote by acknowledging, "I learned my lesson."

Sen. Spark M. Matsunaga (D-Hawaii) was the swing vote on an issue that threatened to derail one of President Reagan's key initiatives. The president had warned that denying him "fast-track" negotiating authority for the free-trade agreement could set back economic and political relations with Canada for years to come.

Under special rules for trade negotiations, the president gets the authority he was seeking unless the Senate panel or the House Ways and Means Committee votes to disapprove it. The tie vote defeated the disapproval resolution, giving the administration a victory.

The close squeak for the president on an issue on which he staked his personal relationship with an ally and neighbor showed that trade still has the potential to be a hot political issue on Capitol Hill.

U.S. Trade Representative Clayton Yeutter applauded the committee action and said a U.S.-Canada free-trade pact offers "a historic opportunity to open markets, expand trade and create jobs" in both countries.

In Ottawa, Prime Minister Brian Mulroney said last night, "I am pleased by today's vote." He added, though, that the strong opposition in the Finance Committee "offers dramatic proof of the protectionist threat" in Congress.

Mulroney agreed to negotiate the trade pact during last year's "shamrock summit" with Reagan.

The committee opposition centered on what members complained was the administration's refusal to consult with Congress on trade. Matsunaga said he originally opposed granting the president special negotiating authority because the administration has been "slighting" Congress on trade.

He said he told Reagan, "Frankly the members on this committee are out to teach you a lesson," and that he would not switch his vote until the president said he had learned that lesson.

Matsunaga said the acknowledgment came during a White House meeting with eight senators yesterday morning, when, according to Matsunaga, Reagan acknowledged, " 'Yes, I learned my lesson. That vote yesterday convinced me.' "

"On that basis," said Matsunaga, "I reconsidered my position."

The president was referring to a procedural vote in committee Tuesday that convinced Majority Leader Robert J. Dole (R-Kan.) and Committee Chairman Bob Packwood (R-Ore.) that the administration lacked the needed votes.

Packwood abruptly recessed the hearing Tuesday to give the White House more time to get the needed vote. Sen. John C. Danforth (R-Mo.), who led the opposition, said he had the votes to kill the agreement yesterday morning.

The Finance Committee had until midnight last night to act on the president's proposal. Under the procedure, considered necessary to negotiate trade agreements, Congress can only approve or disapprove an agreement, not change it.

The president intensified his pressure on the committee this morning, inviting Sens. Danforth, Packwood, Dole, Matsunaga, Max Baucus (D-Mont.), John Heinz (R-Pa.), Lloyd Bentsen (D-Tex.) and David Boren (D-Okla.) to a White House meeting. At the meeting were President Reagan, Vice President George Bush, Secretary of Treasury James A. Baker III, Yeutter, National Security Adviser John M. Poindexter and Chief of Staff Donald T. Regan.

"Enormous pressure was brought to bear on senators by very distinguished people," said Danforth.

The administration argued that Canada was a firm friend of the United States, was one of the few countries that supported the air strike against Libya and had helped get American diplomats out of Tehran during the Iranian hostage seizure.

"Canada is the unfortunate victim of differences between the administration and Congress on trade issues," said Packwood, who with Dole originally opposed giving the president the Canadian authority.

Danforth and Baucus, however, complained that committee members know too little of the administration's aims in the free trade talks and accused the White House of being too willing to please Canada at the expense of American businessmen and farmers.

"The administration has not really earned our confidence to proceed with free-trade negotiations with Canada," said Danforth.

"This senator," he added, "is going to be very, very, very hard to please" when the administration asks for congressional approval of the agreement in about two years.

"We want to be a partner, not a puppet, in these negotiations," added Bentsen.

Danforth also insisted that the trade issue is "alive and kicking" in Congress despite administration opposition to bringing out a bill this year, when it could face protectionist pressures. "We are not prepared to let them coast along," he added. "We will be far more vocal and far more assertive in developing a fair deal for American trade than we have in the past six months."