hierophante: The 'solution' is the blunt and obvious 27. Qg6, which forces 27...Qe8 to prevent mate on f7. "Yawn." You might say.
But the firecracker is 28. Qh6!, where the Q is immune to capture because of a Boden's Mate with 29. Bxh6++.
The possible defences involve creating a flight path for the Black K, with the most obvious move being 29...Bb4. If so, then White wins with 29. Qh8+ Ke7 30. Qxg7+ Kxe6 31. Qxb7 b5 32. Qxa6+, certain to promote as many pawns as he desires.
Alternatively, and likely best, is that Black defends with 28...Qh5! which not only instantly terminates all of White's attacking options, but signals the start of an attack on White's king position. The Q exchange is thus White's best option, with 29. Qxh5 Nxh5 30. Bc7 b5 31. axb5 axb5 32. Bd7 b4 33. h4, and the balance of power in the endgame tilts heavily in White's favour.
There is good cause to assess White with a big edge with three pawns for the piece, much more active Bishops, and a White can start to mobilize his K-side pawns in coordination with activating his King. The endgame in this line holds far better chances for White than the variation that occurred in the actual game.