The Senate last night approved a foreign aid authorization that contains qualified victories for the Reagan administration in its quest for a free hand in sending assistance to countries once barred from receiving it.

The Senate voted 55 to 42 to endorse a House-Senate conference report that would remove restrictions on aid to Pakistan, Chile and Argentina.

But the final version contains restrictions on aid to Pakistan that the administration strongly opposed, even up to the final day when a dispute developed over what exactly the conferees had agreed on.

As it finally passed, the authorization permits the administration to renew military and economic assistance to Pakistan, which had been barred from receiving it because it is suspected of trying to develop nuclear weapons. The ban had cut off aid to non-nuclear countries trying to build atomic weapons.

A restriction insisted on by the House would cut off aid if a country engages in nuclear fuel enrichment or reprocessing. The president could waive that and continue aid, but the waiver could be overridden by a concurrent resolution of Congress.

A second restriction would be even tighter in the case of a country detonating, receiving or transmitting a nuclear device. The president could waive the cutoff for only 30 days, and all aid would cease unless Congress acted to continue the assistance program.

The Reagan administration had quietly opposed both restrictions when the conference committee met. Late yesterday afternoon, it appeared that the restrictive House language had been omitted from the conference report, casting doubt on its final approval. But the language was restored to suit House members and the report seems assured of final House approval today.

Aid to Pakistan has been a key element in the administration's support for foreign aid for the past two weeks. But the White House had hoped to win a repeal of the ban without having its hands tied in any other manner.

The authorization bill contains $100 million for Pakistan, the first installment on the administration's proposed $3.2 billion package of military and economic assistance. The measure generally has had strong congressional support because of the presence of Soviet troops in Afghanistan, which borders Pakistan.

The administration won a freer hand on reopening aid to Chile and Argentina, which had been barred on human rights grounds, but the result of floor action this year and the conferees' report is to force the president to report extensively to Congress on developments in those countries.

In the case of Chile, the bill's final language insists that in order to send aid the president must certify that it is in the national interest, that Chile has made significant human rights progress, and that Chile is not abetting international terrorism.

The final version also requires the president to report on whether Chile's government is taking steps to bring to justice persons indicted for the murder of Orlando Letelier, the former Chilean ambassador who was assassinated by Chilean agents in Washington in 1976.

The ban on aid to Argentina was lifted with a provision that the president must certify that aid is in the national interest and that the government there is making significant progress in human rights affairs. In making that determination, the president must consider Argentine efforts to provide information on citizens who have "disappeared."

According to committee sources, the conferees agreed to lift the aid restrictions for Argentina and Chile as part of an understanding that the administration would not press for similar new latitude on aid to anti-government groups in Angola.