Two games, similar winning strategy

I originally posted the first of these two games in showcase, as it was the strongest opponent I have beaten on Chess.com. However, after beating another opponent of very similar level with the SAME sacrifice strategy, I wanted to get some analysis done. How did I beat two strong opponents while down a peice? Was it good positional play on my part, or was it more the errors of my opponents that allowed me to win the matches? I'd like to get some expert opinion on this so that I know whether I can use this is a strategy regularly, and how the strategy might be improved. So, the first game:

Another common element, as philidor_position pointed out in Showcase for the first game, is that my win did not come from the side where I initially made the sacrifice attack. Interesting that this happened for both games.