President Reagan's embattled policy in Central America cleared a key hurdle last night as the Democratic-controlled House approved an administration-backed package of aid for the Nicaraguan rebels.

The 221-to-209 vote reversed a House vote of 222 to 210 in March that rejected Reagan's plan to provide $70 million in military aid and $30 million in nonlethal "humanitarian" assistance to the counterrevolutionary rebels, or contras.

After beating back two Democratic efforts to overturn or limit the aid package, the House voted 249 to 174 late last night to send the measure to the Republican-controlled Senate.

The plan could still face difficulty in the Senate, but the main obstacle to Reagan's policy has always been the House.

Last night's vote represented a strong turnabout from the March rejection in what was seen as possibly Reagan's last chance to keep a contra aid package alive this year. The battle was preceded by intensive lobbying by administration officials, including the president, who made a televised appeal for support Tuesday and talked by telephone with lawmakers until shortly before the key vote.

The House's reversal, accomplished with the help of 51 Democrats, thus rescued Reagan's policy from what appeared to be near extinction three months ago, leading to forecasts last night that it will soon be implemented.

"There is no question of a clear consensus on the Senate side for some immediate military aid to the contras," House Minority Leader Robert H. Michel (R-Ill.) said in predicting eventual enactment of the package.

Speaking to a Las Vegas fund-raiser last night, Reagan said the vote was "only Round One -- but oh boy, what a round."

Upon his arrival in California, where he will be vacationing for five days, Reagan said the vote "signals a step forward in bipartisan consensus in American foreign policy . . . . Once again, members of both parties stand united in resisting totalitarian expansionism and promoting the cause of democracy."

In winning one of his toughest congressional tests, Reagan picked up since the March vote the support of five additional Republicans and six extra Democrats for his version of the contra aid package. The margin in the critical vote was larger than either side had predicted.

Rep. Albert G. Bustamante (D-Tex.), one of the lawmakers who switched sides, said he became convinced during a recent trip to the region that "there will be no peace in Central America until internal reform is forced" on Nicaragua's Sandinista government.

"I came away convinced we need to continue to pressure the Sandinistas," he said.

The other lawmakers who came over to the administration side were Democrats Les Aspin (Wis.), Mario Biaggi (N.Y.), Carroll Hubbard Jr. (Ky.), Marilyn Lloyd (Tenn.) and Richard B. Ray (Ga.), and Republicans Bill Frenzel (Minn.), Larry J. Hopkins (Ky.) John G. Rowland (Conn.), Olympia J. Snowe (Maine) and Chalmers P. Wylie (Ohio).

The aid package, which the House adopted as an amendment to the fiscal 1987 military construction appropriations bill, would provide $40 million in aid to the contras, including military funds that would be available beginning Sept. 1. It would also provide $20 million in aid on Oct. 15 and a final installment of $40 million next Feb. 15.

The three installments would total $70 million in military funds and $30 million in humanitarian assistance, the amounts Reagan initially sought in March. The measure would also lift a congressional ban on covert activities by U.S. intelligence agencies against Nicaragua, and provide $300 million in economic development funds to four Central American democracies.

The administration-backed plan, sponsored by Reps. Mickey Edwards (R-Okla.) and Ike Skelton (D-Mo.), was adopted as a substitute to an aid package crafted by Rep. Dave McCurdy (D-Okla.) and other moderate Democrats.

The McCurdy plan, strongly opposed by the White House, would have provided $30 million in humanitarian aid to the contras immediately, but made the $70 million in military assistance subject to a second vote in Congress on Oct. 1 or later.

The only skirmish that Democratic opponents won during the long debate was the narrow adoption of an amendment to the aid package that would bar U.S. personnel from entering Honduras or Costa Rica within 20 miles of the Nicaraguan border to train or otherwise aid the contra forces.

The prolonged debate over the issue reached an emotional peak early last night as Rep. George M. O'Brien (R-Ill.), who is suffering from cancer, was brought to the House floor in a wheelchair to cast his vote for the Reagan aid plan. His presence, and Reagan's intense lobbying, were signs of the administration's determination to win.

The floor debate that preceded the critical vote raged over familiar arguments on Central America policy that have been heard in Congress almost from the outset of the Reagan administration.

Supporters of the administration package said military aid to the contras was vital to prevent Nicaragua's Sandinista government from consolidating a Soviet-backed base in the heart of Central America. Delaying military aid until a second congressional vote in the fall, they argued, could doom the contras and encourage Nicaraguan pressure on neighboring democratic states.

"Once the contras are gone, there won't be any other solutions for the American government except diplomatic protests or the insertion of American troops" into the region, Rep. Dick Cheney (R-Wyo.) said.

"Let's end the vacillation," Michel said. "Systematic delay is not a policy, it's paralysis. Let's have the guts to fight communism and nurture democracy in our hemisphere now, not later."

Critics of administration policy described the contras as an ineffective "ragtag force," and zeroed in on a recent General Accounting Office report that suggested the possible misuse of much of the $27 million in humanitarian aid Congress approved for the contras last year.

"We are being asked to vote to send $100 million to drug dealers, gunrunners and embezzlers," Rep. David E. Bonior (D-Mich.) said.

House Majority Whip Thomas S. Foley (D-Wash.) said the House was being asked to support a "proxy war" against another government and predicted that this would lead to a "tragic and irreversible" course toward the introduction of U.S. troops in Central America.

The vote climaxed an intense, three-month struggle during which the House Democratic leadership made tactical compromises in an attempt to hold together a majority coalition against military aid to the contras.

When the House rejected Reagan's original proposal in March, Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) kept McCurdy and other wavering moderate Democrats on board by promising them a second chance to vote for a contra aid package that they crafted as an alternative to the administration plan. The second chance was set for April 16, but never took place. House Republicans, charging that the procedures for that showdown were stacked against them, resorted to a parliamentary maneuver that in effect prevented the McCurdy plan from coming to a vote on the floor.

O'Neill, however, was still bound by his promise to the Democratic moderates, setting up the climactic third test on the issue yesterday. But before the struggle came to a head on the floor, the Democratic leadership made one more tactical retreat, in effect conceding defeat on the question of humanitarian aid to the contras in an effort to delay if not kill outright the military assistance portion of the package.

The leadership did this by striking a deal with McCurdy that incorporated his aid plan into the military construction appropriations bill. Thus, the only way to prevent some contra aid package from clearing the House would be to adopt a substitute proposal by Rep. Lee Hamilton (D-Ind.), providing only refugee relief funds, or to reject the entire appropriations measure on final passage.

This maneuver angered Democratic liberals who opposed any aid for the contras. Demonstrating their displeasure, 122 Democrats voted against adoption of the ground rules for the debate under which the McCurdy plan was made a part of the appropriations bill.

"I believe we've been compromised too much," said Rep. Tony P. Hall (D-Ohio), but most Republicans supported the arrangement. "At least we get one clear, fair shot" to adopt the Republican-backed aid package, Minority Whip Trent Lott (R-Miss.) said.

In the end, the House rejected the Hamilton proposal 245 to 183. It also rejected, 225 to 198, an attempt by Rep. Michael D. Barnes (D-Md.) to bar the release of any funds to the contras until the administration provided a full accounting of the $27 million in humanitarian aid that was approved last year.

The administration also made some concessions leading up to yesterday's vote. It agreed to delay delivery of "heavy weapons" to the contras until February and to provide economic assistance funds to Nicaragua's democratic neighbors.

But there was no compromise on making release of the military funds subject to a later vote by Congress, the key difference between the Edwards and McCurdy aid packages.