Pawn and Two: <psmith> Fritz 12 confirms that 37.Qb3 is winning for White: (3.52) (21 ply) 37.Qb3 Nf4 38.Bxc5 Qxc5 39.Qb7 Qf8 40.Ne7+ Kh8 41.Nxd5 Nxd5 42.Bxd5 Qxa3 43.g3.
However, 37.Qf3 is also very strong, and winning: (2.68) (21 ply) 37.Qf3 Nf4 38.g3! Bxf2+ 39.Rxf2 Nh3+ 40.Kg2 Qxf2+ 41.Qxf2 Nxf2 42.Bxd5+ Rxd5 43.Ne7+ Kf7 44.Nxd5.
As indicated, 38.g3! was the winning continuation.
After 38.Rd1?, Fritz indicates the position is equal: (.00) (20 ply): 38.Rd1? Kf8 39.Bxd5 Rxd5.
After 38.Rd1?, Black played 38...Bxb4, and Fritz indicates the position is equal after: (.00) (22 ply) 39.axb4 Kf8 40.Bxd5 Rxd5 41.Rxd5 Nxd5 42.g3, or 39.Bxd5+ Rxd5 40.Rxd5 Nxd5 41.Qxd5+ Kf8 41.Qd8+, or 39.g3 Kh8 40.Bxd5 Rxd5 41.Rxd5 Nxd5 42.axb4 Nxb4.
After 38.Rd1 Bxb4, 39.Ne3 appears to give White a small advantage, but after a few accurate moves, Black can obtain an approximately equal position: (.63) (23 ply) 39.Ne3 Kh8 40.Nxd5 Bd6 41.Ne3 Qc7 42.g3 Nh3+ 43.Kf1 Ng5 44.Qg4 g6! 45.Nd5, (.00) (20 ply) 45...Qc5 46.Nxf6 Rf8 47.Rd5 Nf3 48.Kg2 Ne1+ 49.Kg1 Qxa3 50.Nd7 Nf3+, or after 45...Qc5 46.Kg2 h5 47.Qe2, (.00) (20 ply) 47...Kg7.
After 39.Rxd5??, the game was clearly lost. As noted, White had several moves that would have retained equality.
After 39.Rxd5?? Nxd5 40.Bxd5 Kh8, if then 41.Ne3 Qxa3 42.g3 Bd2 wins.