President Reagan, in rescuing the tax-overhaul bill from defeat this week at the hands of rebellious Republicans, turned to the weapon that has rarely failed him: his formidable persuasive power.

In a last-ditch plea, Reagan came through by converting enough skeptical Republican House members to revive the major domestic priority of his second term. But he also illustrated what insiders acknowledge as a continuing and troublesome aspect of his presidency: excessive delegation to competing factions on strategy and tactics.

While Reagan rushed in Monday afternoon with a personal appeal to rebellious Republicans and carried the day, he also played a significant role in creating the crisis, sources said.

On the night the House Ways and Means Committee approved the tax bill, Reagan's principal advisers quarreled over strategy while the president, exhausted by the Geneva summit and unaware of the dispute, went to sleep.

"It's one of those 'Rocky' stories," said a Republican source involved in the tax-bill negotiations. " 'The Gipper' is down, he's on the mat, it so happens he was knocked down by his own team . . . . The Gipper gets up, and here it is! He's risen once again . . . . It's just a godsend in terms of timing."

Yesterday, senior administration officials took turns savoring their victory and praising the president's performance.

"We're proud of it," White House spokesman Larry Speakes said. Reagan's appearance was the "foremost" factor in the victory, Treasury Secretary James A. Baker III said.

Similar assessments came from Deputy Treasury Secretary Richard G. Darman, who teamed with Baker in a massive lobbying operation on behalf of the bill, and from Dennis Thomas, the chief White House legislative strategist.

Even as they engaged in self-congratulations, officials conceded that Reagan had been fortunate and that the staff work was less than perfect. "It's a good thing we're not being judged on the basis of style points," one official said. "This is the Reagan luck of bad luck turning into good," another added.

This official said the tax bill would have been overshadowed by the deficit-reduction bill approved by Congress and received relatively little media attention if it had passed last week. Instead, Reagan's comeback in the face of a Republican rebellion again cast him in the role of effective leader.

Conflict within the administration erupted Nov. 22, a day after Reagan returned from the Geneva summit, when he was presented with an options paper listing choices. He approved a Baker recommendation calling for his qualified endorsement of the committee bill after a Republican substitute was voted down. The decision was to be communicated by letter to Congress.

Reagan left the Oval Office and returned to the White House residence late that afternoon. The bill was coming up in committee that night, and the Republican leadership, especially Whip Trent Lott (R-Miss.), wanted the bill to die. The dissident Republicans won agreement by Thomas and, through him, of White House chief of staff Donald T. Regan to delay an endorsement.

Baker and Darman returned to the Treasury, awaiting a signal from the White House before they went to Capitol Hill. Sources said that Regan eventually agreed to an endorsement, though not a letter, but that Thomas wanted to wait.

Thomas has since said that an endorsement would have harmed Reagan because it would have put House Republicans in confrontation with their president rather than with the Democratic majority's tax bill. By now, it was late at night, the president had gone to bed and none of the advisers woke him for a decision.

By the time Reagan endorsed the bill 12 days later, the Republican rebellion was in full swing. Stung by defeat on a procedural vote in which all but 14 Republicans deserted the White House, Thomas and Regan discussed the high-risk strategy of having the president go to the Hill.

Baker, Darman and legislative liasion M.B. Oglesby agreed that it should be done, setting the stage for Reagan's dramatic appeal to GOP House members Monday.

While many Republicans did not change their views on the spot, one member, Rep. Henry J. Hyde (Ill.), emotionally declared his trust in Reagan, who vowed to veto the final bill if it did not meet his criteria.

Afterward, one administration official said some members realized that "they put themselves, their president and their party in a terrible position by what they'd done" in openly defying Reagan.

To reinforce this feeling, the White House and the Republican National Committee alerted Reagan activists to dangers posed by the rebellion and urged them to pressure House GOP members.

Meanwhile, Baker and Darman lobbied wavering members far into the night, working in the office of House Minority Leader Robert H. Michel (Ill.) But the key player, as so many times in the past, was the president.

"Never underestimate Ronald Reagan," said Kenneth M. Duberstein, his former legislative lobbyist.

Summing up the struggle, a White House official said, "A major victory is when you survive today's battles to fight tomorrow."