Possible to force win an Endgame as White?

In this game, I make a pretty terrible blunder with 31. Qxg8?? where I should have played the simple 31. Rxf7!! and end the game with a very healthy material advantage. After 32. Kh2 however, my opponent also made a mistake with 32. ...Qg7?? where I was able to win (Note that my opponent lost from time, due to him/her waiting for their last ~4 minutes). What I'm curious on though is whether or not 31. Qxg8 really is a game ending blunder or not and whether White will be able to force a win by promoting a pawn or capturing the Black queen. After running computer analysis, the position turned up equal with Black's next best move as 32. ...Qg5 (after waiting a minute or two for the computer to decide without any forseeable changes in its calculation). Any extra analysis is appreciated. 

Yes, you threw away and easy win and your opponent then returned the favor by throwing away a clear draw.