The idea of using the h-pawn as a battering-ram is by no means a new one, but h2-h4 has never been played before in this position.
13...Ncb4
Accepting the sacrifice with 13...Bxh4 14.Nxh4 Nxc3 15.bxc3 Qxh4 16.Rd3 would have given White a very dangerous attack.
14.h5 b6 15.Ne5 Bb7
16.a5!?
White's attack has come to a grinding halt, since he can't get his white-squared bishop working on the b1-h7 diagonal. Kramnik therefore seeks play elsewhere.
16...b5
16...bxa5 17.Ba4 Rf8 18.Nd7 Re8 19.Nc5 Bc6 20.Bxc6 Nxc6 21.Nxe6! looks like fun for White.
17.h6 g6 18.Ne4 Nc7?!
18...Rc8 was much more natural, considering White wants to jump in on c5.
19.Nc5
19.Bd2 Bd5 20.Bxd5 Ncxd5 21.Rac1 looked like an interesting alternative.
19...Bd5 20.Ra3 Nc6 21.Bxd5 Qxd5 22.Ncd7 Rad8
22...Bxa3?? was not on because of 23.Nf6+ winning the queen.
23.Nxc6 Rxd7 24.Nxe7+ Rexe7 25.Rc3 f6 26.Be3 Kf7
27.Rdc1
This position looks about level to me. Black still has the superior structure, but he has no real prospects of winning the isolated d-pawn. And White's control of the only open file on the board should count for something.
Black is probably holding after 42...Rxd6 43.cxd6 (43.Qxd6 Qe6) 43...Ke8 44.Qb3 g5! The desperate try 45.Qg8+ Kd7 46.Qa8 ends in perpetual check after 46...Qd5 47.Qxa6 Qd1+.
43.Qh5+ Ke7 44.Qd1 Kf7 45.Rd7+! Kg6
Black is in big trouble after 45...Re7 46.Qb3+ since 46...Qe6? loses a piece to 47.Qxe6+ Kxe6 48.Rd6+.
46.Rg7+ Kxh6 47.Qd7
Some computers were suggesting 47.Rc7 (idea Qd7) during the game.
47...Re5 48.Qf7 Rd5
49.Kh1
A fancy attempt at zugzwang that doesn't quite pan out. 49.b4 Nd8 (49...Nxb4 50.Kh2 Qe5+ 51.g3 Qf5 52.g4 Qe5+ 53.Kg2 and White mates.) 50.Rxh7+ Qxh7 51.Qxd5 would have made life much more difficult for Black.
49...Nd8
49...Nxa5? 50.g4!! Rd1+ (50...Qf3+ 51.Kh2) 51.Kh2 Qe5+ 52.Kg2 and yet again, Black finds himself up the creek without a paddle.
Decentralising the queen allows too much counterplay. The more sensible 56.Qd5 would have retained some winning chances.
56...Qd7! 57.Kh2 Qd3 58.g3
White has to allow perpetual check after 58.Qxa6 Qh7+ 59.Kg3 Qh4+ 60.Kf3 Qh5+ 61.Ke4 Qh7+ since his king ends up in a bad way after 62.Kd4 Qc2! One point is that 63.Qxb5 loses the queen to 63...Ne6+ 64.Kd5 Nc7+.
58...Nf7!
Heading for e5. As any Russian schoolboy will tell you, the queen and knight work very well together!