Sunday Chess Puzzle, November 7

I'm trying a new thing. Every Sunday, I will post a puzzle taken from one of my chess games. Today's puzzle begins in the following position. For reference, I played with the white pieces.

Black to move. In this position, black has mate in 3, and has nothing to worry about. However, in the game, black played Ra8??, and lost his chance at a win! White is now able to draw the game. What is white's idea, and how does white eke out a draw?