White indeed found the only way to lose, by playing the Q-sac 37.Qxf8+. He could have simplified to a trivially won K+P ending (thanks to the outside passed h-pawn) by just trading all the remaining pieces on f7. Instead, White's "cute" Q-sac should have actually lost the game for him. Black, with seconds left on his clock, missed that he could simply take a R with his N (38...Nxf7) before playing ...Qg6. After that White would have to lose either his B or R, so it's all over.