You Aren't Safe Until the Clocks are Stopped
White: Ke3, Rc4, Ba4, p's a2, d7, f4, g3, h2.
Black: Kg7, Rd6, Bd8, p's a6, f7, g6, h5.
I don't know if White's winning here, but Black's future is likely to consist of a good deal of suffering before achieving a draw - if it's even possible. Ideally, White would like to bring the king to the queenside (preferably c8) without trading rooks, but achieving that isn't going to be easy. Still, White is completely safe, right?
The game continued 40.Bc6 Bb6+ 41.Ke4 f5+ and now White realized that continuing forward with 42.Ke5 allows Bc7, when White is lucky that he's only losing his d7 pawn (the position after 43.Ba4 Rxd7+ 44.Ke6 Rf7 should be a routine draw). Therefore, Avrukh decided to save his d-pawn with 42.Kf3. Sensible...except that after 42...Rd2 it was time to resign, as mate is unavoidable (43.g4 h4 44.gxf5 gxf5 45.Rc5/Rc2/Rd4 Bxc5/Rxc2/Bxd4 46.Any Rf2#).
One expects this sort of thing from online 1-minute chess, but in a non-time trouble situation with strong GMs? Errare humanum est!