The Republican-controlled Senate cleared the way for the final installment of President Reagan's 1981 tax cut to take effect as planned this Friday as it killed a bill from the Democratic-controlled House to limit the benefit to a maximum of $720 per return.

The vote was 55 to 45, almost entirely along party lines.

Withholding rates will now be reduced about 10 percent in all brackets, effective on work performed Friday. For married workers with two children making $20,000 a year, take-home pay will go up a little over $4 a week on the average. For similar workers making $30,000 the increase will be just under $9. Single taxpayers will take home a little over $7 a week more if they are at the $20,000 level, about $14.50 if they make $30,000.

The withholding reduction puts fully in place the 25 percent tax rate reduction that was the centerpiece of Reagan's original economic program, and which he has called the mainspring of economic recovery.

The Democrats proposed for what they called reasons of fairness and deficit reduction to cap the cut. Their bill would have raised about $6 billion a year, mostly from taxpayers with adjusted gross incomes over $50,000.

By killing the House-passed bill the Senate left Congress in an awkward position, in that the budget resolution approved by both houses last week calls for $12 billion in new revenues next fiscal year and $73 billion by fiscal 1986.

There is now no revenue-raising measure of that size in sight, and neither the House Ways and Means Committee nor the Senate Finance Committee is expected to meet the July 22 target date in the budget resolution for drafting one.

Ways and Means Chairman Dan Rostenkowski (D-Ill.) said he would schedule hearings for mid-July to "take the temperature of the committee" on how to raise the money.

Finance Committee Chairman Robert J. Dole (R-Kan.), who has referred to the budget resolution's revenue requirement as a "dead cat dumped into the lap of this committee," said again after yesterday's vote that he wants to raise funds by removing unspecified "loopholes" and "special tax breaks," not by raising rates for individuals.

There was little suspense on the Senate floor yesterday, in part because Majority Leader Howard H. Baker Jr. (R-Tenn.), after joining with GOP moderates and breaking with Reagan over the budget last week, had exacted a pledge that they would stand fast on the tax bill.

Reagan also had promised to veto a tax cut cap and the Democrats even in the House lacked the votes to override him. Since everyone knew all this, yesterday's vote was more a test of political loyalties than of fiscal policy.

Only three Republicans voted with the Democrats in favor of limiting the tax cut. They were Arlen Specter (Pa.), John Heinz (Pa.) and William S. Cohen (Maine). Four Democrats--J. Bennett Johnston (La.), Howell Heflin (Ala.), David L. Boren (Okla.) and Edward Zorinsky (Neb.)--voted with the Republicans.

The Senate debate sounded like a tape recording of the debate in the House last week.

Democrats, led by Sen. Bill Bradley (N.J.), argued that curtailing the reduction was a "fair" way to raise $6 billion in revenue, imposing a small burden on a relatively affluent group for the benefit of the nation as a whole, and that the tax cut as it stands is a giveaway to the wealthy with borrowed money.

"It would be nice to give everyone a 50 percent tax cut, but we simply can't afford it" in an era of $200 billion deficits, Bradley said.

Dole, leading the Republican opposition, said the measure was just another Democratic tax increase. "We'll see in a few minutes who wants to raise taxes," he said before the vote. "That's what it's all about. They want to raise taxes for some people because they happen to make a little more money than other people."