A classic problem endgame: Queen and pawns vs two rooks and pawns.
30... Rd2xb2
Holding the Black b5-pawn will turn out to be critical, though I did not foresee it at this point.
31. Qa6e6 Kg8f8 32. Qe6b6 Rd8d2
The broad strategy for the rest of the game is now set: Black is threatening to mate the White king on the back rank (or squash him against the Black king-side pawns if he flees forwards); White must try to force perpetual check. For the next 15 moves, the White queen and the Black king play cat and mouse. Where will the Black king find refuge?
At last the White queen has run out of checks; the Black king has found refuge on f4 of all places. Note that the Black pawns are holding the crucial squares a4 and d4, protecting the king from checks.
49. Kh2g1
If instead 49. Qa8 or Qg7, Rxg2+; 50. QxRg2, RxQg2+; 51. KxRg2, Ke3 etc. and Black promotes a pawn before White's h-pawn promotes.
49... Rf2xg2 50. Kg1f1 Rg2c2 51. Qa7a8 Rc2c1
White played quite well, given the ratings differential and the problematic endgame. 0-1