Despite last-minute, telephoned appeals from President Carter to Key members, the Senate Finance Committee yesterday rejected the hospital cost-control plan the president has called a crucial test of congressional will to fight inflation.

By 11 to 9 the committee adopted a proposal by Sen. Bob Dole (R-Kan.) to table the administration plan.

But administration supporters promised to move their fight for the proposal to the Senate floor, where they won last year, though the House didn't act.

In the House Ways and Means Committee yesterday, administration supporters staved off a different kind of attempt to bury the measure.

They did so by only an 18-to-18 tie vote, but some hospital lobbyists, fighting to kill administration proposal, conceded that the administration probably has the votes to get the bill out of Ways and Means.

The amendment that failed to pass, offered by Rep. James R. Jones (D-Okla.), would have postponed debate for a week while he and other members wrote a new bill. Jones wanted to abandon any federal control over hospital spending, except over federal and state funds for Medicare and Medicaid patients. These amount to one-third of hospital spending.

And he wanted to use the week to write a bill to establish a new system of health insurance rules and tax incentives to make employers and employes more cost-conscious, and to promote medical plans that compete for patients by cutting costs.

Many committee members said this was a good idea. But 17 apparently agreed with Rep. James M. Shannon (d-mass.), who said the idea behind Jone's move was to defeat the Carter plan, while "getting some members off the hook politically" by enabling them to say they are still for cost cutting.

The fight on the Senate side for a modified version of the administration bill was led by Sen. Gaylord Nelson (D.Wis.). Committee Chairman Russell B. Long (D-La.) voted with Nelson.

This fulfilled a recent pledge by Long to the president to swing his support to Carter on this issue, and, to a considerably lesser degree, on a start on national health insurance.

But Sen. Herman E. Talmadge (D-Ga.) voted against the administration plan, as did Sens. Mike Gravel (D-Alaska) and Lloyd M. Bentsen (D-Tex.) and a host of committee Republicans.

Nelson's bill would have put a federal ceiling on hospital spending only if the hospitals failed to limit their spending. This federal spending exceeded 1978 figures by more than 11.6 percent.

American hospitals' total spending rose 13.2 percent in the first quarter of 1979, compared with the same period in 1978. An article in yesterday's Washington Post erroneously said the increase was 12.5 percent.)

But the hospitals' nationwide Voluntary Effort held the spending increase in March, the last month of the quarter, to 12.5 percent, and an announcement of a similar figure for April is expected today from Voluntary Effort headquarters in Chicago.

Nelson argued that passing a hospital cost-control bill would force hospital economies that would save $32 billion in the next five years, according to a Congressional Budget Office estimate.

The Finance Committee agreed to report out a Talmadge bill that would tighten federal reimbursement to hospitals for Medicare and Medicaid patients. The senator's aides said these changes could save the government nearly $1 billion a year in the next five years, citing CBO estimates.

An HEW official said the savings probably would be more like $600 million to $700 million a year, far less than the savings promised by the administration plan.