Anatoly Karpov made the score 2-0 yesterday in the world chess championship match in Merano, Italy. The 30-year-old defending champion defeated his perennial challenger, 50-year-old Viktor Korchnoi, in a 57-move game played in two sessions Saturday and Sunday. This gives Karpov enormous advantages, not only in the score but in the psychology of the match, which will be won by the first player to score six victories. "It's just an extremely horrible start for Korchnoi," said former U.S. champion Robert Byrne.

This was not the worst position Korchnoi has ever been in during his championship matches with Karpov. In the 1978 match in the Philippines, he was trailing by 4-1 after game 17; then he began to rally in game 21 and had evened the score at 5-5 by the end of game 31 -- before losing game 32 and the match. But action was much slower in that match, with the first seven games ending in draws and an even score of only one victory apiece after game 12.

The challenger's spokesman, Emanuel Sztein, said in a press conference yesterday that Korchnoi is under "terrible pressure" because his family is still being kept in the Soviet Union despite his efforts to get exit visas for them. Korchnoi has not seen his wife, Isabella, or his son, Igor, since he defected from the Soviet Union in 1976. Igor is in a prison camp, serving a 30-month sentence for avoiding military service. According to Sztein, Korchnoi's wife said in a recent phone conversation that Igor had been beaten severely.

Korchnoi's play, as in the first match game last Thursday, could have been interpreted as a symptom of his preoccupation with other matters. As in the first game, he seemed uncertain where to put his queen and made several moves which, while not exactly mistakes, were far below his usual sharp level of play. His first serious mistake -- serious enough to lose the game for him -- came on his 34th move. Once his f-pawn was displaced, Karpov was able to capture his a-pawn with impunity on move 35: Rxa7. If Korchnoi had taken the rook (35. . . .Qxa7), Karpov could have replied 36. Qxe6ch, capturing a knight, recovering the sacrificed rook, and even threatening a quick checkmate in some variations (36. . . .Kf8; 37. Bd6ch). The game was over, for all practical purposes, by the time it was adjourned after black's 41st move.

When the game resumed yesterday, Karpov played slowly, methodically and unspectacularly, like a boa constrictor at lunch. He consolidated his position and gradually reduced his opponent to helplessness.

The third game of the match is scheduled to be played today.

Following are the moves in the second game of the Karpov-Korchnoi chess match in Merano, Italy. White: Karpov. Black: Korchnoi.

1. e4, e5; 2. Nf3, Nc6; 3. Bb5, Nf6; 4. 0-0, Nxe4; 5. d4, Be7; 6. Qe2, Nd6; 7. Bxc6, bxc6; 8. dxe5, Nb7; 9. Nc3, 0-0; 10. Re1, Nc5; 11. Be3, Ne6; 12. Rad1, d5; 13. exd6 e.p., cxd6; 14. Nd4, Bd7; 15. Nf5, d5; 16. Nxe7ch, Qxe7; 17. Qd2, Qh4; 18. Ne2, Rfe8; 19. b3, Re7; 20. Ng3, Qf6; 21. f3, Be8; 22. Ne2, h6; 23. Bf2, Qg6; 24. Nc1, d4; 25. Nd3, Qf6; 26. Bg3, Rd7; 27. Re5, Qd8; 28. Rde1, Rd5; 29. Rxd5, Qxd5; 30. Re5, Qd7; 31. Qe1, Rc8; 32. b4, Qd8; 33. Ra5, Qd7; 34. h3, f6; 35. Rxa7, Qd5; 36. Ra5, Qd7; 37. Ra7, Qd5; 38. Ra5, Qd7; 39. Qe4, Bf7; 40. Qf5, Re8; 41. Kh2, Qb7; 42. a3, Rd8; 43. h4, h5; 44. Nf2, Qd7; 45. Ra6, Qe8; 46. Qa5, Bg6; 47. Nd3, Kh7; 48. Qb6, Rc8; 49. a4, Bf5; 50. a5, c5; 51. bxc5, Bxd3; 52. cxd3, Nxc5; 53. Ra7, Qg6; 54. Rc7, Rxc7; 55. Bxc7, Nxd3; 56. Qxd4, Ne5; 57. Bxe5, and white resigned.