Congress yesterday averted another government shutdown and gave high-level federal officials a pay raise as the Senate voted final approval for an omnibus spending bill that meets President Reagan's demand for at least $4 billion in domestic appropriations cuts.

Easily beating back a series of Democratic amendments to restore funds, the Republican-controlled Senate voted 60 to 35 to approve the measure and send it to Reagan, who is expected to sign it Monday.

An identical version of the bill won approval of the Democratic-controlled House on Thursday, when a unified GOP, allied with conservative Democrats, delivered the same coalition-style majority that enabled Reagan to win his more impressive budget victories earlier in the year.

Shortly after the Senate vote, Reagan issued a statement hailing the bill--a so-called continuing resolution to sustain through March 31 those agencies whose regular appropriations bills have not passed--as "a difficult step forward in this nation's struggle to restore responsible economic and fiscal policy," but warning that even tougher budget battles lie ahead. "We must not rest," said Reagan, who is already at work on further cuts in next year's budget. "The nation expects continued follow-through."

Reagan's House and Senate victories this week were more symbolic than real, focusing at the end on a difference of about $1 billion out of a total budget of more than $700 billion and a projected deficit of about $100 billion for fiscal 1982.

On top of earlier budget cuts of $35 billion Reagan had asked for another $16 billion in deficit reductions, including $8.4 billion from a 12 percent cut from domestic appropriations that he had proposed earlier in the year.

Because of congressional resistance, he settled for $4 billion in domestic cuts, along with whatever military savings Congress approves in a Defense appropriations bill next week.

The votes this week enable Reagan to prepare for next year's budget wars with at least theoretical majorities in both houses, although there were rumblings from Republicans as well as Democrats that little more can be squeezed from domestic appropriations.

"I think all members will agree that we have reached the bone on discretionary programs so that there is nothing more to cut," said Senate Appropriations Committee Chairman Mark O. Hatfield (R-Ore.). "If there has been any encouragement in this dreary exercise, it has been the realization . . . that the budget can only be brought under control if entitlements, defense spending and tax expenditures are given the same scrutiny and brought under the severe constraints that discretionary programs have suffered."

Among the few winners were 40,000 to 50,000 government officials whose pay has been frozen at $50,112 since 1979. Under the bill, their pay will be raised on Jan. 1 to as much as $57,500 for the highest-level senior executives, with proportionately smaller increases for lower-level employes. The price tag is estimated at $165 million.

Among those hardest hit, on the other hand, were the General Services Administration and 50 relatively small government agencies--including the White House and its Office of Management and Budget--that will suffer relatively larger cuts than many other agencies, according to congressional sources.

The reason is that, unlike most agencies, they were cut by the 12 percent proposed by Reagan even before Congress applied its own 4 percent cut in order to come up with the $4 billion savings, for an overall 16 percent cut.

"People have been calling in all day in absolute shock," said Robert Honig, director of the Federal Government Service Task Force for the House and Senate, warning that some agencies may be severely crippled. Asked how the White House and the OMB have responded, an appropriations committee staff member said, "They're biting their tongues."

The agencies may have at least some of their money restored if Congress approves the Treasury-Post Office appropriations bill, which includes their regular funding, before it adjourns for the year. Passage is viewed as uncertain.

Congressional approval of the omnibus bill came five days before expiration of the emergency funding that had to be provided last month after Reagan vetoed an earlier resolution as too expensive. That veto resulted in a one-day shutdown of most of the government, which neither Congress nor Reagan seemed eager to repeat as they cooperated this month on a compromise.

The vetoed resolution saved only about $2 billion. House Democrats had proposed $1 billion in additional savings. The GOP substitute that passed added another $1 billion, for an overall total of $4 billion in savings.

After Senate Democrats failed in about six hours of foredoomed efforts to add back money for programs ranging from infant care to mine safety, several complained bitterly about the new cuts.

"If the administration devoted as much time and energy to bringing down interest rates as it does to bringing down every government program in sight, we'd be making a lot more headway in fighting inflation and unemployment," said Assistant Minority Leader Alan Cranston (D-Calif.).

In yesterday's Senate vote, only two Republicans voted against the $4 billion cut, while seven Democrats voted for it. Virginia's senators voted for the cut. Sen. Paul S. Sarbanes (D-Md.) opposed it. Sen. Charles McC. Mathias Jr. (R-Md.) did not vote.

As it headed toward an anticipated adjournment on Tuesday, the Senate in effect put off all the major so-called "social issues," including abortion, prayers and busing, until next year.

Abortion had already been delayed. A proposal to keep the federal courts from ordering busing to achieve desegregation, delayed for months in a filibuster by liberals, was put off yesterday. So was a proposal to allow prayers in public schools, when the Senate failed by one vote to invoke cloture to end a filibuster on that issue.