The House gave final approval yesterday to the massive tax on domestic crude oil that President Carter proposed last year and sent it to the Senate, where the industry's supporters will make one last effort to cut it back.

The bill, which would bring in an estimated $227 billion over the next decade to recoup part of the higher prices resulting from Carter's decision to lift oil price controls, was approved by the House 302 to 107. The key vote was a refusal, 227 to 185, to send the bill back to a House-Senate conference to try to give independent producers a better break. Supporters feared the fragile compromise would collapse and the bill die if it were sent back to conference.

The Republican effort to recommit the bill would have instructed House conferees to accept a Senate provision exempting the first 1,000 barrels a day produced by an independent. Independents do more of the exploring for oil. By definition they engage only in production, not in refining or distribution like the majors. Their supporters argued that the tax break was needed to encourage exploration to lessen reliance on foreign oil.

But managers of the bill contended that House conferees already had leaned over backward to ease the burden on independents. They will pay only 10 percent of the total revenue expected, and they include many relatively big businesses.

"This is no Mom and Pop" proposal, said Rep. Charles Vanik (D-Ohio); "this is a Big Daddy amendment." Rep. Sam Gibbons (D-Fla.), a conferee, said the House had already given the independents too much and he wouldn't vote to give any more no matter what the House did.

The 1,000-barrel exemption could mean millions of dollars a year in profits to big independents.

Oil men who have been in town the last few weeks in hard hats with rigs parked at the bottom of Capitol Hill are trying to put the independent exemption back. Sen. Henry Bellmon (R-Okla.) and others will champion their cause when the Senate takes up the conference report next week.

Many House Republicans wanted to kill the bill on grounds that it would stifle production. But supporters said more oil wells were drilled last year than in any of the last 20, an indication that producers are making money.

Rep. Robert Michel (Ill.), a leading candidate to be the next Republican leader of the House, supported the tax compromise. He said it is the price that must be paid for decontrolling domestic oil prices, which the industry and administration have contended in the key to more production. The bill was also supported by the Republicans' senior tax specialist, Rep. Barber Conable (N.Y.), and their top energy man, Rep. Clarence Brown (Ohio).

The bill also includes a long list of tax credits for businesses that install energy-saving equipment, and a shorter list of residential credits. The maximum tax credit for installing a solar heating system at home would be increased from $2,200 to $4,000.

To encourage savings, the bill would exclude from taxation the first $200 received in interest from a savings account.

The bill recommends that 60 percent of the revenue be used for income tax cuts and the rest be divided between helping the poor pay their energy bills and energy production or conservation. But this must be finally decided by other legislation.

The only Maryland members voting to send the bill back to conference were Republicans Marjorie Holt and Robert Bauman. All eight Maryland members then voted for the bill.

All Virginia members voted to send the bill back to conference except Democrats Joseph Fisher and Herbert Harris. The delegation then divided 5 to 5 on final passage, with Republicans William Wampler, G. William Whitehurst and Paul Trible joining Fisher and Harris in voting for it.