Win from this position w/o sac or promotion?

I was playing in a live chess game today when I came upon this position as black (see above). I ended up saccing my Queen and promoting a pawn, which I thought was lame play on my part - but I couldn't think of a way to win by taking his pawn then mate, or whatever. Just wondering if anyone could help me out, because this could easily happen in a game when I didn't have the advantage of the two passed pawns.

Cheers.