Meeting in their first face-to-face campaign debate, Virginia Republican Sen. John W. Warner and his Democratic challenger, Edythe C. Harrison sparred repeatedly here tonight over defense issues important to this state's military-minded economy.

Warner, a member of the Senate Armed Services Committee who is seeking his second term in the Nov. 6 general election, accused Harrison of supporting "unilateral" nuclear disarmament that would endanger the nation's security.

Harrison, hoping the debate would give her admittedly underdog candidacy a boost, charged Warner had misstated her position on arms control and hammered away at his support of "big ticket" weapons systems such as the MX missile and B1 bomber that she said don't work while conventional military readiness deteriorates.

"The Soviets are paranoid. . .but the Soviets are not suicidal," said Harrison. "We're seven minutes away from destruction," she said, suggesting the U.S. should do more to get nuclear arms talks under way.

Warner based his claim largely on a Harrison brochure printed last winter, calling for a systematic end to the arms race in which the U.S. should "challenge our adversaries to follow our lead."

The hour-long debate, sponsored by ther Virginia League of Women Voters, also touched on several other issues, including the nation's huge budget deficits, Warner's opposition to the Equal Rights Amendment and the effect of federal budget cuts on education and other social programs.

The debate, before an audience of about 750 persons at the Pavilion Convention Center here, was shown on a local commercial station, broadcast on a statewide network of radio stations and was telecast in Northern Virginia on two educational channels. Three newsmen asked questions of the candidates, who were not allowed to question each other.

Asked about mixing religion and politics -- an issue that has dominated the presidential campaigns recently -- both Warner and Harrison said they believed in the "wall of separation" between church and state.

In a news conference following the debate, Harrison remarked that "when we run into trouble is when people speak for God."

In his own news conference, Warner declined to criticize state GOP chairman Donald Huffman of Roanoke for suggesting last week that liberal political thought in this country "is moving away from God," while conservatives are "moving toward God."

But Warner noted that Democrats, particularly some black politicians, have sought to use religion to advantage. He pointed to both Jesse L. Jackson, a minister strongly supported by black churches and Bishop L.E. Willis, an influential Norfolk businessman and clergyman who led Jackson's surprisingly strong showing in Virginia's presidential caucuses.

After the debate, representatives of both sides said they were pleased with their candiate's performance, but Harrison and her supporters were clearly excited.

Trailing in name recognition, campaign organization and far behind in fundraising, Harrison had sought to show that she could discuss issues and dispel efforts by Republicans and even some Democrats to paint her as a "loose-cannon" liberal.

Often speaking in homey, straightforward sentences, Harrison appeared comfortable throughout the debate. In contrast, Warner was cut off three times by the moderator after his answers ran over the allotted time.

On the nation's budget deficit, Harrison said the country "goes shopping every day" and spends a half billion dollars it doesn't have. Breaking with Democratic presidential candidate Walter F. Mondale, she said she would oppose raising taxes until the budget, including military spending, is combed for cuts.

Harrison, a civic activist and former General Assembly delegate from Norfolk, drew one of the few laughs from the auditorium crowd that had been admonished to be quiet. In response to a question about the ERA, Warner appeared to back away from his remarks last summer that he might support a revised version of the ERA.

"You can't be a little bit pregnant," Harrison said with a smile, stressing her own support for the failed amendment.

Meeting just minutes from one of the nation's largest naval installations, Warner at one point acknowledged that he has been unable in five years to get a controversial bill passed that would dredge the Hampton Roads harbor here and make it more competitive economically and more efficient militarily.

But he said his experience on the Armed Services Committee is vital to Virginia's economy. He noted that about 15 percent of the nation's defense spending affects Virginia.

Throughout the debate, Warner stressed his 25 years of public service, including a term as undersecretary of the Navy and his support of President Reagan's foreign and domestic programs. Reagan is generally thought to hold a wide margin of support in Virginia over Mondale.

Warner said the nation's economy is better under Reagan, with sharp drops in inflation and interest rates from the Carter years. Warner, who repeatedly referred to the Carter-Mondale administration that preceded Reagan, never mentioned Harrison by name, referring to her only as "my opponent."