karlzen: Masterful play - an old classic. White played four okay moves and after Ng3 opting for nothing it was over. Nimzo exchanges light-squared bishops, then queens (something similar happens in a line of the French Advance var: 1.e4 e6 2.d4 d5 3.e5 c5 4.c3 Bd7!? 5.Nf3 Qb6 6.Be2 Bb5!? 7.0-0 Bxe2 8.Qxe2 Qa6) and continues by putting all his pawns on light squares, blockading á la himself.
The endgame was played flawlessly and note that 42...Ne3+ with the idea to take on b2 after checks and exchanging the win is not that straight-forward (on Nc3 black has to play a4-a3 and the manoeuvre his knight over to e4, take on g3 and f4 by using the c-pawn as decoy and then win with the two connected passed kingside pawns). In any case, Nimzo chose another road to the full point.
Also note that the natural 43...Nxc3 44.bxc3 Ba3 doesn't quite work. Black will play his bishop to b2 and king to e4 when which white must block with his king on e4. Then white can only move his bishop which will have to leave the queenside for f2-e1. Black crawls closer with his bishop and gets to c1 but no further. The only winning try after that is Bxf4!? but white will stop the passed kingside pawns with the bishop and continue blocking the black king in the centre. There is a line where black forces his way in to the white position though (after Bxf4) but white can hold (I'm only 99% sure so be aware). I'm sure that extensive analysis of the position has been published somewhere.
Figure a position where black has just sac'ed on f4 (his king is on f4) and white's king is on e2, his bishop at f2 with white to move. White plays (52).Bh4 g3 53.Bf6! (this diagonal is very important because in the case of Kxc3 white has d4-d5+! tricks) 53...Ke4 54.Be5! f4 55.Kf1 Kf3 56.Bd6 Kg4 (intending f3 and g2 followed by simply Kg4-f5-e4xa2) 57.Ke2! f3+ 58.Ke3 and the position is a draw (58...f2 59.Ke2 Kh3 60.Kf1 Kh2 61.Be5 and black can't advance his g-pawn).
If 56...Ke3 (above) instead, then 57.Be5 Kd2 58.Kg2 Kc2 59.Bxf4 Kxc3 (if instead 59...Kb2 then white sacs on the a-pawn, takes on e6 and queens the d-pawn just in time) 60.Be5! Kc2 61.Kxg3 Kb1 62.d5! exd5 63.a3 Ka2 64.Kf3 Kxa3 65.Ke3 and the position is again a draw, e.g. 65...Ka2 66.Kd2 Kb1 67.Bd6 d4: 68.Ba3 Ka2 69.Bc5 or 68...c3+ 69.Kd3 c2 70.Kxd4 c1Q 71.Bxc1 and Kc3=. Another nice line is: 65...Kb3 66.Kd2 a3 67.Bd4 a2 68.Be5 and a draw is the result.
This shows how difficult endgames can be and how well Nimzowitsch played it.