Sen. Albert Gore Jr. (D-Tenn.) was the best performer at a Democratic foreign policy debate last week -- at least by the lights of a small but potentially significant slice of Southern swing voters, according to a survey released yesterday by the Democratic Leadership Council.

Gore, who set himself apart in the DLC-sponsored encounter on Oct. 5 with his enthusiastic support for U.S. shows of military force in Grenada and the Persian Gulf, had entered the debate in third place among the voters sampled, with 12 percent of the support. After the debate, he was in first place with 38 percent support.

The candidate with whom he sparred most frequently that evening, Rep. Richard A. Gephardt (D-Mo.), was the other big gainer in the survey. He entered the debate supported by just 8 percent of the viewing sample, in fifth place, and emerged with 19 percent of the support, in second place.

Massachusetts Gov. Michael S. Dukakis' support declined from 14 to 11 percent, that of Sen. Paul Simon (D-Ill.) remained flat at 11 percent, Jesse L. Jackson's dropped from 23 percent to 9 percent, and former Arizona governor Bruce Babbitt's grew from 0 to 3 percent.

Those surveyed by the DLC, an organization of moderate Democrats, were residents of Charlotte, N.C.; Jacksonville, Fla., and Atlanta, who voted for President Reagan in 1980 or 1984, and voted for a Democratic Senate candidate in 1986.

This so-called crossover voter comprises 10 to 15 percent of the overall Southern electorate, and is considered important to the Democratic Party's hope of improving its showing in a region where it has carried only one state in the last two presidential elections.

The survey sample consisted of 490 voters interviewed before the DLC debate and 295 who were reinterviewed afterward. Among the principal findings:This swing bloc is more ideologically diverse than is sometimes thought, with 33 percent calling themselves conservatives, 49 percent moderates and 14 percent liberals. The sample was slightly more upscale in education and income than the national norm, and 13 percent of it was black. These swing voters think Republicans do better, by a 53-to-25 ratio, at assuring the nation will be respected around the world, and, by 56 to 26, at keeping it prosperous. Voters rank keeping inflation under control and reducing the deficit as more important than increasing national defense spending. They want the next president to hold the line, not raise, defense spending. The debate improved the overall impression of the Democratic field. The percentage of the group who said they would vote Democratic next November jumped 11 points, to 42 percent from 31 percent.