Why did white win this endgame?

I'm just confused by the following game.  Why did I win?  Where did we both screw up?

I don't think you messed up by taking the pawn...although your opponent blundered like a second grader, good finish.

nice endgame hithere2, you won because black didn't move in the right order

on the first move Rxh2  g1=Q ! the game still even

 I think that's offensive towards second graders.

You also made a huge blunder with 3. Qxe6+, 3. Qh8+ followed by 4. Qg8+ wins the black queen. 

When the opponent played 12. ...Rc5 and let you take the pawn, that is where he went wrong.

1. bondiggity makes a great point: you missed a tactical shot on move 3 that would have "won" the game for you.

2. You were grossly behind on material, down a Rook, but your opponent made two fundamental endgame mistakes:

A. Misuse of his Rook

B. Misuse of his King

Your opponent didn't bring his King into the game until very late. Your 2 pawns + King = 5 points and his Rook + pawn = 6 points, so by not using his King, you weren't actually down that much material. 

Starting at move 7, black should have been moving his king instead of doing  useless checks. Black still had a pawn there and the rook ensures the black king never reaches the queening square.

Wow!  I didn't notice any of this!  I'll be taking advantage of this forum a lot more now.

obviously a very low ranked game, i would have promoted first and ignored the rook, and while black was promoting i would have the advantage