The Senate leadership, backed up at the last minute by the State Department, narrowly turned back a get-tough-with-Cuba resolution yesterday after a lengthy debate registering conservatives' impatience with administration efforts to contain communism in Latin America.

A 41-to-39 vote to table the resolution, originally considered innocuous, was achieved only after lobbying by Majority Leader Howard H. Baker Jr. (R-Tenn.), a bipartisan appeal from Foreign Relations Committee members and circulation of a hastily drafted statement of opposition from the State Department.

The non-binding resolution, proposed by Sen. Steven D. Symms (R-Idaho), would have restated the 20-year-old congressional pledge to use military force if necessary to combat Cuban-style subversion in the Western Hemisphere. That warning stemmed from the Cuban missile crisis and a subsequent agreement on Cuba reached between the United States and the Soviet Union.

The resolution's advocates claimed that that agreement had been violated repeatedly and that Cuba has exported support for revolutions in Nicaragua, Guatemala and El Salvador without forceful opposition from American governments, including the Reagan administration.

The debate and close vote reflected pressures from conservatives who have been demanding, since January, full-scale committee hearings and floor discussion on a Cuban policy. Their concern has been heightened recently by reports that the administration has moved toward opening negotiations with Cuba, a development viewed with suspicion by some of the administration's strongest supporters in both chambers.

They chose as a vehicle for airing their complaints the Symms resolution, which merely restates the 1962 language about using force, a statement subscribed to by every administration since then.

Symms argued that if the Senate balked it would be sending incorrect signals to Cuba about U.S. determination to resist subversion. "Fidel Castro would say, 'Well, the United States Senate doesn't stand up for what the current law is,' " he said.

He said Cuba had violated the understandings of 1962 repeatedly, and claimed that recent remarks by Soviet President Leonid I. Brezhnev suggest that the Soviet Union is trying to "blackmail" the United States with hints of introducing nuclear missiles in Cuba.

Sen. Charles H. Percy (R-Ill.), chairman of the Foreign Relations Committee, replied that there is no emergency requiring any resolution before committee hearings are held, and said its emphasis on armed responses against Cuba conveys the impression that military force is the "preferred" American tactic for dealing with Latin American problems.

Percy also said that restating militaristic language used in 1962 might undercut the usefulness of the War Powers Act, passed in 1973 to restrict an administration's use of American forces overseas without congressional approval. The Symms resolution, he said, could be construed by some president bent on intervention as an "authorization in advance" for sending troops into Latin America, and likened it to the Tonkin Gulf resolution used by the late Lyndon B. Johnson to send troops to Vietnam.

"The people do not want Latin America to become another Vietnam," Percy said. He also promised that the Foreign Relations Committee would hold hearings by early May on several Latin American issues, including Cuba.

During most of the debate the position of the administration remained unclear, and at times both sides implied that they were supported by the State Department.

Shortly before the mid-afternoon vote, however, a letter from a State Department congressional liaison officer, Alvin Drischler, to Baker was circulated on the floor. It said the department did not find the Symms' resolution "helpful."

The resolution had been introduced as an amendment to a bill to permit television and radio coverage of Senate deliberations, a long-pending measure that has been debated acrimoniously for weeks, off and on. Senate leaders indicated yesterday that the radio-TV measure probably will come to a vote next week.