The Reagan administration won the first skirmish in the Senate battle over extension of the 1965 Voting Rights Act yesterday as a Senate Judiciary subcommittee voted along party lines for a simple 10-year extension of the act.

The vote put the subcommittee sharply at odds with 65 senators, including 10 Republican committee chairmen, who are cosponsoring a version of the bill passed by the House last fall by a 389-to-24 vote. The major difference between the two is that the version approved by the House and introduced in the Senate by Sens. Edward M. Kennedy (D-Mass.) and Charles McC. Mathias (R-Md.) extends the act forever, rather than for 10 years, and would provide an easier standard for proving violations.

Civil rights leaders charged yesterday that the version approved by the subcommittee would "severely jeopardize the voting rights of millions" of blacks and other minorities.

But the administration, including President Reagan and Attorney General William French Smith, have warned that the extension being cosponsored by a majority of the senate would lead to racial quotas in state legislatures, city councils, school boards, and even in congressional elections.

The chief point of disagreement is the standard for proving a violation. Until 1980, most civil rights lawyers proved their cases by simply gathering evidence that a local election system had the "effect" of discriminating against blacks. But in 1980 the Supreme Court ruled--in a case involving the city of Mobile, Ala.--that the law is violated only if the officials responsible for the election laws "intended" to discriminate.

The administration and the subcommittee want the law to contain an intent standard while the House and most of the Senate are supporting an effects standard.

Sen. Orrin G. Hatch (R-Utah), chairman of the subcommittee on the Constitution, which voted yesterday, warned during the meeting that an effects standard would lead to racial quotas, to a "country in which considerations of race and ethnicity intrude into each and every public policy decision."

Under this test, he said, any government system could be held to be discriminatory if minority candidates fail to win elections in proportions to their population ratios, even if no discrimination were intended.

Sen. Dennis DeConcini (D-Ariz.) insisted that an effects test will not lead to racial quotas "or any of the other dire consequences suggested by the bill's opponents."

Sen. Strom Thurmond (D-S.C.), chairman of the Judiciary Committee, said yesterday he would try to schedule action in the full committee within the next 30 days, saying he wanted action as quickly as possible to "underscore our commitment to the right to vote and allow us to turn our attention to . . . a healthy economy and a strong national defense."

Most of the senators involved say they expect a major fight when the bill reaches the full committee. Nine of the 18 members are cosponsors of the Kennedy-Mathias bill, and at least two others have not yet stated their position.

Sen. Charles E. Grassley (R-Iowa) supported the administration position yesterday in the 3-to-2 vote, but made it clear that he plans to seek a compromise position. "I'm reserving the right to modify my vote in the future," he said.

Thurmond added that there would be an attempt in the full committee to work out a reasonable "bailout" provision for jurisdictions in parts of 22 states with a history of racial discrimination that now must get preclearance from the Justice Department before making any changes in their election laws.

He said the Kennedy-Mathias provision to free local election districts from the preclearance requirement after a period of good behavior does "nothing but raise more questions . . . . Preclearance would be extended forever. That's clearly unconstitutional and unacceptable."

Both Thurmond and the administration have asked for an easier bailout procedure.