The Senate yesterday smiled on the nation's independent oil producers and voted to exempt most of their production from President Carter's proposed "windfall profits" tax on oil.

The exemption was voted 53 to 41, -- worth an estimated $10 billion over the next 10 years -- over objections from the Carter administration, which is pushing to increase, not decrease, the Senate bill's orginal anticipated yield of $138 billion by 1990.

Liberal-to-moderate Democrats, many of them facing reelection battles next year, helped give the independent producers their victory, the oil industry's forst of any consequence in nearly two weeks of slow-moving Senate action on the controversial tax bill.

The Senate also abandoned its Finance Committee's plan to earmark future revenues from the tax by use of special trust funds, voting instead to leave future spending decisions to the normal authorizing and appropriating process. The action reflected concern over committee prerogative more than any dispute over spending priorities.

After the vote on the independent producer exemption, Sen. Lloyd M. Bentsen (D-Tex.), its chief sponsor, said he expected few if any other major ammendments to be adopted. "I don't see any major ones that will prevail," he told reporters.

Administration lobbyists agreed that further weakening amendments are unlikely to pass, but they held out some hope for strengthening amendments that together could add about $65 billion to anticipated revenues from the Senate measure.

This would help the administration is stiffening the tax when the Senate attempts to work out a compromise with the House, which earlier voted for a bill that would raise an estimated $277 billion by 1990, twice as much as the proposed Senate measure.

The Senate refused Monday, 32 to 50, to substitute the House proposal for its own Finance Committee's $138 billion bill.

Prospects for an early windup of the tax fight grew dimmer yesterday as Sen. John Tower (R-Tex.) a staunch toe of the tax, introduced an amendment of vast mischief-making potential to extend the windfall profits levy, now aimed solely at-the proceeds form oil price decontrol, to all American industries. It might take "a great deal of talk," said Tower, smiling.

Bentsen's amend exempts the first 1,000 barrels a day of production by independent drillers, who differ from the major oil companies in that they do not also refine and market oil products.The Independent Petroleum Association of America, which lobbied vigrously for the exemption, said that 98 percent of the 12,000 independent producers estract fewer than 1,000 barrels a day and thus would be totally exempt from the tax.

Unlike the House bill, the Senate Finance Committee proposal exempted all newly discovered oil and the first 1,000 barrels a day from so-called "stripper" or low-production wells.But Bensten argued that this exemption was not enough to keep the independents, which drill 98 percent of the nation's exploratory wells, drilling at full tilt.

While Bentsen contended that any revenue loss from the exemption would be made up "dollar for dollar and then some" by reinvestment in energy discovery, opponents argued that independents have enough money already and that the exemption would not produce, as one of them put it, "one single drop more oil." Sen. Daniel P. Moynihan (D-N.Y.), who led the fight against the exemption, described it as "legislation for a privileged thousand firms."

In other action on the bil, the Senate agreed to earmark $1 billion from the windfall tax revenues for revitalization of the rail industry. It dis so after rejecting $10 billion for the rail industry.

Among the senators up for reelection next year who frequently vote against the oil industry but who supported the exemption for independents yesterday were George McGovern (D-S.D.), Frank Church (D-Idaho), Dale Bumpers (D-Ark.), Birch Bayh (D-Ind.) and Ernest F. Hollings (D.S.D.). Washington area senators were divided on the issue, with Harry F. Byrd Jr. (Ind.-Va.) and John W. Warner (R.-Va.) voting for the exemption and Charles Mathias (R.-Mid.) and Paul S. Sarbanes (D-Md.) voting against it.