The position reminded me of Jeremy Silman's "fox in the chicken coop" model endgame technique that went by the name "outside passed pawn" when I was young. But, in the heat of the moment, there seemed more to consider.
White to move
While playing blitz, I often fail to take the time to calculate pawn races. After 1.Kd4 Kd6. White wins by going after the g-pawn. The white h-pawn promotes while the black a-pawn is on a2. Moreover, White still has the triangulation option if Black plays 1...Kb5, 2.Kc3!
I played 1.Kc3, and after 1...Kb5 2.Kb3 Kc6 3.Kb4 reaching the diagram position with Black to move. 1.Kc3 was the second best move, but it was clearly winning and needed no calculation.
3...Kd6 4.b5 and Black resigned.