In this game Kasparov gives up a pawn for nothing in particular at move 7. He gives up another one at move 14, but this also doesn't seem to achieve much. His position seems to slip downhill a bit so he comes up with the best practical chance: 29.Rc7, which gives up a rook with check.

VK misses 36...gxf6 37.Nxg6+ fxg6 38.Bd5 Qe8 39.Qg8+ Ke7 40.Qe6+ Kd8, which wins.

He also misses - on the last move before the time control - 40..Be5, which wins more or less on the spot. Kasparov should have played 40.Kf3; perhaps there is an error in the game score though I don't think so.

After 33.Kg3, Fritz gives the evaluation 9.42!!

The first real mistake after that was 36...Bxf6?, which was completely unnecessary, as <offramp> points out above.

Then Kasparov makes a mistake of his own with 38.Kxf2?, when 38.Qh8+ would probably draw after the exchange of queens.

And then, Korchnoi misses 40...Be5, which is obviously completely winning. I can only imagine the Korchnoi was down to a few seconds on the clock to be able to miss that.

The final mistake was 41...Qf6? which throws away any kind of winning chances, although the position may still be drawn.

First
Analysis by Stockfish 260819 64 POPCNT:
1. -+ (-9.30): 29...a1Q 30.Rxa1 Rxa1+ 31.Kg2 Ra2 32.f6 Ng6 33.Bxg6 hxg6 34.Ne7+ Rxe7 35.fxe7 Qa8 36.Qf3 Rxf2+ 37.Qxf2 Bxf2 38.Kxf2 b5 39.Rb7 Qc8 40.Ke2 f5 41.gxf6 gxf6 42.Kd2 Kf7 43.Rxb5 Qh3 44.e8Q+ Kxe8 45.Rb8+ Kf7 46.Rb7+ Kf8 47.Rc7 Qxh2+ 48.Kc3 Qg3+ 49.Kb2 Qf2+ 50.Rc2 Qb6+ 51.Kc1 Kf7 52.Re2 Qg1+ 53.Kc2 Qg5 54.Rd2 Qf4 55.Kc1

2. -+ (-9.28): 29...a1R 30.f6 Ng6 31.Bxg6 hxg6 32.Qg4 Rxf1+ 33.Kxf1 Re5 34.Ne7+ Rxe7 35.Rxe7 Qb6 36.Qf4 gxf6 37.gxf6 Qb5+ 38.Kg2 Ra1 39.Qxd4 Qf1+ 40.Kg3 Qg1+ 41.Kf3 Qh1+ 42.Kg3 Rg1+ 43.Kf4 g5+ 44.Ke3 Re1+ 45.Kd3 Rd1+ 46.Ke3 Rxd4 47.Kxd4 Qf3 48.Kc4 Qxf2 49.Kb5 Qc5+ 50.Ka4 b6 51.Kb3 Qd5+ 52.Kb4 Qf5 53.Rc7 Qxf6 54.Kb3 Qe5 55.Rc2 f5

Second
Analysis by Stockfish 260819 64 POPCNT:
1. -+ (-9.32): 34...Rf3+ 35.Kg2 Rf2+ 36.Kg3 h6 37.fxe7 Qa8 38.Qd1 Nc6 39.gxh6 Rb2 40.Qf1 Be5+ 41.Kg4 Qe8 42.Qf5 g6 43.Nf6+ Kh8 44.Qxg6 fxg6 45.Nxe8 Nxe7 46.Nc7 Kh7 47.Kf3 Bxh2 48.Ke3 Kxh6 49.Kd3 Kg7 50.Nd5 Nf5 51.Nc7 Kf6 52.Bd5 b5 53.Bb7 Be5 54.Be4 Ke7 55.Bxf5 gxf5 56.Ke3 Kf7 57.Nd5

2. -+ (-9.10): 34...h6 35.fxe7 Qa8 36.Qd1 Nc6 37.gxh6 Rb2 38.Qf1 Qe8 39.Qf5 Be5+ 40.Kg4 g6 41.Nf6+ Kh8 42.Qxg6 fxg6 43.Nxe8 Nxe7 44.Nc7 Kh7 45.Kf3 Bxh2 46.Ke3 Kxh6 47.Kd4 Kg7 48.Kd3 Kf7 49.Nd5 Nf5 50.Kc4 b5+ 51.Kd3 Be5 52.Nb6

Third
Analysis by Stockfish 260819 64 POPCNT:
1. -+ (-10.08): 36...gxf6 37.Nxg6+ fxg6 38.Bd5 Qe8 39.Qg8+ Ke7 40.Qe6+ Kd8 41.Qxd6+ Qd7 42.Qxd7+ Kxd7 43.Bxb7 Rb2 44.Bd5 Rb5 45.Bc4 Rxg5+ 46.Kf3 Be5 47.h4 Rg3+ 48.Ke2 Ke7 49.Bd3 Rg4 50.Kf3 Rf4+ 51.Ke3 Kf7 52.h5 gxh5 53.Be2 h4 54.Bd1