37. Kg3 Qd6+; Kh3 or Kh4 Qh6 threatening mayhem on the h-file.
37. f6 Rf7 followed by hxg4 and g3+ and the WK has nowhere to hide. If, say, 38. Qf1 hxg4; Kg3 to stop this then Qd6+; Kh4 g3+ and White is toast. In some variations B can just play ...Rxf6 instead of ...hxg4, and again the WK ends up with nowhere to hide.
(I'm a patzer, or more precisely a rusty club-level player; the above is the result of some experimenting with a strong computer program. I may have missed important things.)
38. f6 Rxf6 39. Rxf6 Qxf6 looks totally hopeless for White, can't defend both h6 and g6
38. g5 Rh6+ 39. gxh6 Rh4+ 40. Kg6 Qf6++
Don't see any other plausible options to prevent 38... Rh6++.
But Anand's 36...g5+ is much easier for a human to play. It's easier to see White's reasonable responses and how to deal with them.
Anand never made a move that let go of his winning advantage, and all the (mild) criticisms of his play are based on moves that computers think win a little faster; but a human should play to win as reliably as possible, and that's what he did.
I am astonished though by Topalov's mistakes capturing the f and e pawns. They were inexplicable, because they're not really tactical errors at all; they simply show terrible positional misunderstanding.