4th Cherry Blossom Classic

I played in the 4th Cherry Blossom Classic over the Memorial Day Weekend.  The tournament did go better than the Philadelphia Open, but I made two mistakes that were easily avoidable. Both games were equal, but I ended up losing because of my blunders. I still ended up tying for 7th place in the Open Section and won $16.67 in prize money.

In the sixth round, I played against a young kid, who currently holds the record for being the youngest national master in US Chess history. After about four hours of play with both players running low on time, we reached the following endgame position.  Can you find how White can get a draw?

1. h3 f3+ 2. Kf2 gxh3 (2... fxg2 3. hxg4 h3 4. g5) 3. gxf3 Kxb5 4. Kg1 

I originally intended to play this line. However, in time pressure, anything can happen, and I became confused. I missed the idea of the g-pawn promoting, and instead played the following variation, losing the game.  Congratulations to my young opponent for playing such a good game.

 1. Kf2 Kxb5 2. h3 g3+ 3. Kf3 Kc4 4. Ke2 (4. Kxf4 Kd3 5. Kg4 Ke2 6. Kxh4 Kf2) 4... Kd4 5. Kf1 Kd3 6. Ke1 Ke3 7. Kf1 Kd2 8. Kg1 Ke2 9.Kh1 f3 10. gxf3 Kf2)