The Senate Energy Committee pumped some life into President Carter's battered energy saving plan yesterday as it approved his standby gasoline rationing proposal, 9 to 8.

Chairman Henry M. Jackson (D-Wash.) predicted Senate approval because the people have accepted the fact there is an energy problem and want machinery in place to deal with a serious shortage before it develops.

The Senate committee vote was influenced by a letter form the administration yesterday, promising that if a rationing plan were put into effect extra gas would be given to rural states where residents must drive long distances to work and have no mass transit.

The House Commerce Committee divided 22 to 20 Wednesday against the standby gas rationing plan, but could conceivably be turned around by the administration's promise of more gas for states with a history of greater need and use. The House committee tried to meet yesterday on reconsidering its rejection but had to adjourn for lack of a quorum. Republicans boycotted the meeting, apparently fearing Democrats would be able to reverse the Wednesday vote.

Both House and Senate must vote approval of the standby rationing plan by May 11 or it will die. It can be called up for a House vote even if the committee refuses to send it to the floor. Even if Congress approves the standby plan, the president's decision to put rationing into effect must be submitted again to Congress where disapproval by either house would kill it.

There has been no gasoline rationing in this country since World War II. The possibility that it may be needed arises from the fact that the United States now imports half its oil, much of it from uncertain sources in the Mideast.

The Senate committee also discussed but put off until next week votes on Carter's request for standby powers to order weekend closing of gasoline stations, which the House committee rejected.

There appears to be almost unanimous Senate committee opposition to weekend closing on grounds that it would hurt everybody without saving much gasoline. The administration had agreed to amend its proposal to permit states to carry out alternative programs that would save equal amounts of gasoline.

Sens. Bennett Johnston (D-La.) and Pete Domenici (R-M.M.) drew up a bill that was a somewhat more complicated version of this proposal. But it didn't appear to have much committee support except from Chairman Jackson.

It provides that when the president decides a serious gasoline shortage exists he shall set a national conservation target ana announce a plan to reach it. States could develop their own plans and carry them out if approved by the Department of Energy. Johnston said this provided more flexibility to meet local needs.

But most other members found fault with it, either for abandoning the "club" of weekend closing, as Sen. Mark Hatfield (R-Ore.) put it, or giving away the power of Congress to decide what should be done.

Both House and Senate Committees have disapproved another Carter plan to permit him to ban use of outdoor advertising lights, which would save an estimated 4,400 barrels of oil a day out of about 20 million consumed. Both committees have approved his other contingency plan to empower him to limit thermostat settings in nonresidential buildings to not over 65 degrees in winter and not under 80 in summer.