Move I thought would break my neck was actually a blunder!

http://en.lichess.org/HuRH3YYImhdP

This is the most absurd case of an engine-analyzed game I've ever encountered. It looks to me as if my opponent is choking me with the last Queen move he just made, mate becomes inevitable and the only viable option would be to resign ... but lo and behold, computer actually calls it out as a blunder! As I'm absolutely clueless on how I could even begin to exploit this "blunder" I figured I might wanna post it here, to see what others would have to say about this position.

How would you salvage this seemingly lost battle, when the engine tells you that you're actually 2.65 centipawns up!?

It's complex position indeed! but black does not have immediate checkmate, so you can counter instead, i think g6 would generate very strong attack against black's king.