You won because your opponent ran out of cards. Happened to me 3 times:
I was shocked the first time it happened to me, because I didn't knew what happened. The game just automatically gave the win to my oponnent. I was playing a heavy card draw deck with Rustbolt the first 2 times it happened, with tons of Kite Flyers, Pots of Gold and Fun-dead Riser. So I guessed it happened because there were no more cards left in my deck.
The 3rd time I was playing as Rose and was facing a Prof. Brainstorm that ALSO had a heavy card draw deck. It happened the same thing, just the other way around. At the start of the turn 16 (or something like that) the game just gave me the victory.
So, it was because of that.
