31.Bd2 Ne5! with the tactical point 32.Rxh6? Rxh6 33.Bxh6 Ng4, picking up the exchange.
31...a4
This screamingly natural move turns out to be a mistake. After the game, Kramnik admitted he'd missed Kasparov's simple reply.
32.bxa4!?
A brave decision, clearly indicating Kasparov's willingness to take chances.
32...Rxc4 33.Bd2 Rxa4 34.Rxh6 Rg8
Should Black have swapped rooks? Tough call. There is a real possibility that the exchange would make White's h-pawn even more dangerous than in the game. But then again, f7 would be safer, wouldn't it?
35.Rh7 Rxa2
At this stage, both players were in serious time trouble.
36.Rxf7 Ne5 37.Rg7 Rf8 38.h3?!
After the game, Kasparov suggested the rather obvious improvement 38.h4.
38...c4 39.Re7 Nd3
40.f7! Nxf2 41.Re8+ Kd7 42.Rxf8 Ke7 43.Rc8
Black draws with ease after 43.Rd8 Kxf7 44.Kxf2 c3.
43...Kxf7 44.Rxc7+ Ke6 45.Be3
Winning a pawn.
45...Nd1 46.Bxb6 c3
47.h4?
Practically the only move that throws away White's chances of winning!
47...Ra6! 48.Bd4
48.Ba7 c2 was no improvement.
48...Ra4
The point. White now has to exchange his h-pawn for Black's c-pawn, resulting in a completely drawn rook ending.
49.Bxc3 Nxc3 50.Rxc3 Rxh4 51.Rf3
Cutting off Black's king, but to no avail.
51...Rh5 52.Kf2 Rg5!
52...Rf5? 53.Rxf5 Kxf5 54.Kf3 and White wins the pawn ending.
53.Rf8
53...Ke5 - draw agreed.
53...Ke5 54.Kf3 (54.g3 Rf5+) 54...Rf5+ 55.Rxf5+ Kxf5 and the pawn ending is a well-known theoretical draw.
½-½
Related articles
The Kasparov - Kramnik index.
The Kasparov - Kramnik FAQ.