What I thought was winning tactic, apparently was mistake I was recently playing a game as black against the Ponziani when this position came up. (I recommend you flip all the boards to show from black's perspective)

Here's the beginning of the game:

[fen ""]
1.e4 e5 2.Nf3 Nc6 3.c3 d5 4.Qa4 Bd7 5.exd5 Nd4 6.Qd1 Nxf3+ 7.Qxf3 Nf6 8.h3 e4 9.Qe3 Bd6 10.d3 O-O 11.dxe4 Nxe4 12.Bd3 f5 13.Bxe4 fxe4 14.O-O Bf5 15.c4 Qf6 16.Nc3 Rae8 17.Bd2 Be5 18.Qg5


In the starting position, both sides are apparently equal (0.0)

[fen "4rrk1/ppp3pp/5q2/3PbbQ1/2P1p3/2N4P/PP1B1PP1/R4RK1 b - - 6 18"]

1... Qb6 2. Bf4 Bxf4 3. Qxf4 Bxh3


After 2.Bf4 black has apparently made a blunder, putting me 90 centipawns ahead. In the game, I spent 5 minutes debating between Qxb2, h6, and Bxf4 finally choosing the last, seeing it as the simplest most effective option. 

Apparently, Bxh3 was a blunder on my part, putting white ahead 90 centipawns. (So this move helped white by 1.8) Only, I cannot understand why? I ended up winning the game with the following moves.

[fen "4rrk1/ppp3pp/1q6/3P4/2P1pQ2/2N4b/PP3PP1/R4RK1 w - - 0 21"]

1. Qg3 Bd7 2. b3 e3 3. fxe3 Rxf1 4. Rxf1 Rxe3 5. Qf2 Rxc3 6. Qxb6 axb6 7.Rf2 g6 8. Kh2 Bf5 9. Re2 Kf7 10. Rb2 Rc2 0-1


I feel like the decision to play Bxh3 was justified and what helped me win the game. Yet the engine disagrees. Could somebody tell me what the problem with Bxh3 was?
First of all, I don't think it is productive to call moves "blunders" when they're just not the best moves according to the computer. Chess is a game between humans. I like to reserve "blunder" for moves that are really terrible.

That said, after 20...Bxh3, Komodo 9.02 recommends 21.Qe3 for White, forcing Black to exchange queens, after which material is equal (remember that you were down a pawn to start with) and it likes White's position better.

It prefers to delay the discovered attack on the queen by playing 20...e3, threatening 21...Bd3 (winning an exchange), which is really hard for White to deal with. Komodo's line is 20...e3 21.fxe3 Bd3 22.Qxd4 Bxf1 23.Qxb6 axb6 24.Rxf1 Rxe3 and Black is up an exchange for a pawn.