President Reagan won the year's first test in Congress on the defense budget yesterday when the Senate Armed Services Committee in closed session voted, 13 to 3, to stick with the full amount he requested.

The vote was in the form of an advisory to the Senate Budget Committee on the maximum Armed Services is likely to authorize for defense in fiscal 1983. The Budget Committee has asked for such expressions of intent from all the Senate's standing committees to guide it in preparing this spring's congressional budget resolution.

Rejected, 12 to 3, before the final vote, sources said, was a motion by Sen. Gary Hart (D-Colo.) to cut defense spending in fiscal 1983 by $5 billion through a $20 billion reduction in new spending authority for the Pentagon.

The three senators who voted against approving the full amount were Hart, Carl Levin (D-Mich.) and J. James Exon (D-Neb.). They reportedly argued that Reagan's defense budget is financial overkill in a period of $100 billion deficits, domestic spending cuts and persistently high interest rates.

Chairman John G. Tower (R-Tex.) prevailed in his argument that the committee should support the president in shoring up U.S. defenses while creating bargaining leverage for arms reductions talks with the Soviets.

The Senate committee action, although good news for Reagan and the Pentagon, is a long way from definitive. It is just the year's first skirmish on the issue.

Congress is now supposed to adopt two budget resolutions each year. The first theoretically comes in May and sets targets for the year ahead. Then the year's actual appropriations bills are supposed to be passed over the summer. Finally, just before the new fiscal year begins in the fall, Congress reviews these appropriations bills, adjusts them as necessary and passes a second resolution that sums them up and is supposed to be binding.

The Senate Armed Services Committee's recommendation yesterday represents its first judgment on how much is enough for national defense in fiscal 1983. The Budget Committee can lower the recommended amount before putting it in the resolution for consideration on the Senate floor.

The House goes through the same process independently.

The Armed Services senators approved the full $263 billion in new spending authority Reagan requested for national defense (including funds for the Energy Department for nuclear warheads) which the administration says translates into $221 billion in actual spending. Its vote signifies that at least one influential corner of Congress is more afraid of the Russians than of federal deficits and unemployment.

Defense Secretary Caspar W. Weinberger has been unyielding as one congressional committee after another has demanded reductions in the Pentagon's new budget. His line is that defense should not be considered part and parcel of government programs; that the Soviet threat is so worrisome that every dollar he is requesting is needed to keep the nation safe.

Weinberger has been backing up that public testimony with private meetings with lawmakers of all political persuasions, including breakfasting with them at his Pentagon dining room where secret and scary pictures and charts of the Soviet military buildup are shown.

He also intends to try to sell the Pentagon's new budget through speeches and highly visible trips, including one to Pacific military bases soon. But he faces an uphill fight, given the sluggish state of the national economy and demands elsewhere in Congress to remove the Pentagon's immunity to deep cuts.