It might sound counter-intuitive, but Black had more chances with all the rooks.
1. e2e4  1... c7c5  2. g1f3  2... d7d6  3. d2d4  3... c5d4  4. f3d4  4... g8f6  5. b1c3  5... a7a6  6. c1e3  6... e7e5  7. d4b3  7... c8e6  8. d1d2  8... f8e7  9. f2f3  9... h7h5 The modern treatment of the position, widely  popularised by Topalov and Cheparinov. 10. f1e2  10... b8d7  11. c3d5  11... e6d5 This capture is a question of taste. 12. e4d5  12... b7b6  13. e1c1  13... d8c7 This novelty was played after a bit more than two  minutes of thought. 14. c1b1 A generally useful move that frees the c1-square for both the  white knight and rook. Ding's position does not seem inspiring. His king  is not safe on either flank. 14... b6b5  15. b3a5  15... d7b6  16. e3b6  16... c7b6  17. a5c6  17... e7d8  18. c2c4 Thanks to the strong establishment of the knight on c6, Carlsen is opening the c-file for his major pieces. The  full control on the light squares guarantees him a long-term advantage. 18... b5c4  19. e2c4  19... e8g8 Finally Black castles into the attack. 20. h1e1  20... f6d7 This  overprotects the e5-pawn but facilitates the g2-g4 advance. 21. g2g4  21... h5g4  22. f3g4  22... d8h4 It seems as Black will block the kingside,  but... 23. g4g5 Brilliant tactics comes to the rescue of Carlsen's  strategy. 23... g7g6  24. e1f1  24... g8g7  25. d2g2 Carlsen calmly prepares the decisive blow along the  f-file. 25... f8h8  26. g2g4  26... b6c7  27. f1f3 A pity! 27... f7f5  28. g5f6  28... d7f6  29. g4g2  29... c7d7  30. d1g1  30... h8h6 Ding solidified his position and  escaped the imminent danger. However, Carlsen still has a strong grip on  the position. 31. a2a3  31... f6h5  32. f3b3  32... h5f4  33. g2c2  33... g7h8  34. b1a2 The world champion avoids the queen  swap as he is the one attacking with the opposite-colored bishops. 34... d7f5  35. c2d2  35... f5e4  36. g1c1  36... h4g5 Missed by Carlsen. 37. c1c3 Now Carlsen loses almost all  his advantage. 37... f4e6 Excellent play! Ding forces the queen swap. 38. d2c2  38... e4c2  39. c3c2  39... e6d4 Not the most accurate. 40. c6d4  40... e5d4  41. b3b6 Best. 41... g5f4  42. b6a6 