That he was "somehow" able to survive the explosion and fake his own death is just another drop in the bucket (and another allusion to Holmes who also survived a similar impossible to survive "death".) It gets a "final episode" hand-wave.
Well, let's consider that there are different types of explosion. When it comes to fires like this, there are two possibilities, deflagration and detonation. A deflagration is a rapid burn but one where the burn propagates subsonically, so there isn't much of a pressure wave generated. A detonation is a supersonic explosion which generates a far more potent shock wave and does much more destruction. Now, since this was a special-effects explosion, just a billow of flame that didn't involve a lot a force or blow out the whole side of the building, we can assume that it was merely a deflagration -- probably what firefighters call a
flashover, a sudden eruption that occurs in a fire in a tightly enclosed space when flammable gases build up to the right density to trigger ignition (
Mythbusters viewers should be familiar with the principle). A flashover generates huge amounts of heat, but not as powerful a shock wave as a detonation, so it is theoretically survivable. However, survival requires diving to the ground and insulating yourself very effectively from the extreme heat, and from what I can find online, even the best firefighting gear provides only about 14 seconds' grace period to get out of a flashover environment.
So House surviving if he was in the building at the moment of the deflagration is highly unlikely but not impossible. Maybe the floor gave way beneath him and he ended up in the basement, and was thus protected from the flashover on the ground floor.
But the most likely explanation is that he managed to get to the back door just before the flashover occurred. Since the danger came only from heat and not from shock waves, he could've been standing right next to the door and not been killed by overpressure shock or shrapnel. It didn't look like he had time to reach another exit before the deflagration, but that could've been a trick of editing, suggesting Wilson and Foreman's subjective perception of the event. Certainly the depiction of the deflagration was unrealistic; it probably wouldn't have had that loud a "kaboom" sound and would've entailed a lot more smoke. So there's some poetic license at play here (as there always is in cinematic explosions).