Yeah, the point is that you still need to be playing chess. The 2150 should have been doing the kind of thinking like in your analysis, solskytz. The 2150 probably normally plays with plans in mind, but maybe he was hoping a little too much for the win to be automatic -- wins aren't always hard, but never automatic, especially against a strong player. You have to figure that Christiansen has just made his one huge blunder of the decade, and so he's going to make sure he doesn't hang something so obvious for the remainder of the game!
A lot of weak players, if they play on in such bad positions, tend to make their positions even worse -- they'll blunder one or two more times because the are so fed up. Strong players still try to find the absolute best move.
So yes, when a 1600 is up a piece against a 1600, the one up a piece will win very often, but that's partly because the 1600 down a piece will continue to not play very well.
I'm generally pretty apprehensive when I need to stop three reasonably advanced, connected pawns supported by their king, with my own rook, even if my king is helping.
That said, I do think that Cobra91's suggestion is also excellent, and would grant white here at least excellent winning chances, if not a certain, rock-solid outright win. Just some precise, cool calculation is required (this kind of positions is exactly where I personally tend to lose my head as the stronger side... certainly a great tip to blitzers who play against me)