Gary Kasparov, the 24-year-old world chess champion, saved his endangered title yesterday in Seville, Spain. Moving his queen and bishop with the sinister grace of a jungle beast, Kasparov seized a stunning 64-move victory to follow his stunning defeat on Thursday.

"I think it was destiny," Kasparov said in a telephone interview shortly after his victory. "I cannot explain it. But maybe it was meant to happen this way. The match was sliding into oblivion, and I would have felt sort of shameful if I had made two draws in the last two games."

For challenger Anatoly Karpov, the match was "a tragedy of one move." By this, he meant that he had missed tactical points only one move deep in Games 7, 11 and 24 of the match.

Karpov had electrified the chess world by winning Game 23 just when it seemed that the match was fading away, not with a bang but a whimper. For one day, it was almost universally assumed that he would win back the title he had lost to Kasparov in 1985.

In a phone interview, Karpov was reminded that he was not the only one who had missed tactical points -- Kasparov had given him some "presents," notably in Game 23. "Yes," he said, "but these mistakes were not so obvious. They were not one-movers; they were mistakes that anyone could make in the heat of a chess battle."

After the crushing conclusion of a 24-game struggle that had begun in October, both players seemed to be responding in character: Kasparov was ebullient and full of energy, Karpov quiet and philosophical.

"That's life," was Karpov's reaction. "I'm guilty; it was my mistake. I left myself with only three minutes for the last 11 moves." He said that failing to win back his lost title was "not fatal." But he was upset that "the match was decided by big blunders."

"Can you hear that?" Kasparov asked at one point, indicating noises outside his window that could clearly be heard on the intercontinental telephone line. "The Spanish kids outside are shooting firecrackers, celebrating my victory." Earlier, as he left Seville's Teatro Lope de Vega after winning the final game and the match, the crowd had greeted him with shouts of "Torero, torero" -- hailing him as a bullfighter, the highest compliment a crowd can give in Seville.

With all the seats for the last game sold, it was shown on Spanish television. The network had planned to intercut the chess game on television with scenes of a Davis Cup tennis match, but a deluge of telephone calls persuaded the television executives to run the chess game without interruption.

At the end of its prescribed 24-game limit, Kasparov's last-minute victory yesterday tied the 1987 world chess championship match at 12-12. This meant that Kasparov would split the prize fund of over $2 million evenly with Karpov, and Karpov could take comfort in the fact that he had not lost the match. But it also meant that Kasparov would keep the title of world champion until 1990, when he will have to defend it against a challenger still to be selected.

Kasparov said that a one-minute ovation he received as he sat down for the last game gave him "moral support."

"The crowd gave me such an ovation," he said, "and suddenly I felt a great responsibility not to desert them -- not to fail the many chess players in the whole world who trusted me and believed in my abilities. I was afraid to fail all those to whom I had promised my victory."

He has also publicly associated his championship with the policies of political openness and economic restructuring forged by Soviet leader Mikhail Gorbachev, and in the glow of victory he said, "Maybe in a small way, what I do through chess makes a small contribution in helping to solve problems in the world."

He said that he thought Gorbachev's meeting with President Reagan in Washington this month had been "very important . . . a gate to bring the people of the two nations closer together."

"This is not the last agreement to be signed between those two countries," he said. "This is just a start. We should work to solve problems together."

Discussing the last game of the match, both players agreed that the critical moment came with the move 33. Qd1. Kasparov claimed that he would still have been ahead if he had chosen 33. Qb5, the point being that the penetration to the 8th rank via the square e8 would be more forceful. But after 33. Qd1, Karpov failed to find the correct move, 33. . . . Nc5. The idea of the defense becomes clear in the following variation: 34. Qd8ch, Kh7; 35. Qxc8, Qa1ch; 36. Kg2, Qxe5.

Karpov said that he had suffered from a "hallucination," which made him imagine an impossible combination. Instead of 35. Qxc8, he calculated "35. Nc6, Qd7; 36. Qxc8, Qxc8; 37. Ne7ch, and white wins a piece." He was obviously hallucinating that the black king was on g8 rather than h7.

Kasparov said that instead of 35. Nxf7, he should have played 35. Bh5. Dutch grandmaster Jan Timman suggested an even more crushing combination for white: 35. Qe8, with the idea 35. . . . Ng6; 36. Be4, and white's attack wins immediately.

In the endgame position, black's chief error was placing his pawns on white squares where they were subject to attack by white's bishop and where they limited the knight's mobility, making him a tragic spectator near the end of the game.

Karpov's plans for the immediate future were stated simply: "Life goes on, and I will have to try to win the World Cup." This is a competition organized by the recently formed Grandmasters' Association, which will involve 24 of the world's leading players in a two-year series of tournaments funded with about $3 million for expenses and prizes. Karpov and Kasparov will both be playing next year in a World Cup tournament in Bilbao, Spain. Kasparov will also participate in a World Cup tournament in Reykjavik, Iceland, while Karpov plays in one in Brussels.

Both players will appear together, along with Timman, the third-ranking player in the world, on Jan. 6 in Rotterdam. They will conduct an enormous simultaneous exhibition, with each grandmaster playing many games simultaneously against ordinary players. Kasparov plans to visit Washington in February, and both he and Karpov will participate in a speed tournament in February in St. John, New Brunswick, part of the massive World Chess Festival that will be held there from Jan. 23 to Feb. 20.

With this match filed away in history, the gears of international chess grind inexorably toward the next world championship in 1990. National, zonal and interzonal tournaments have been held to trim the next crop of candidates to a manageable size, and the survivors -- 14 players, including U.S. grandmaster Yasser Seirawan -- will be playing one-on-one knockout matches during the St. John tournament in January and February. This will reduce the number of candidates to seven at the quarterfinal level, where Karpov will join the competition, working to get another shot at Kasparov and the crown.

Lubomir Kavalek is a grandmaster and former contender for the world chess championship. Washington Post staff writer Joseph McLellan contributed to this report.