At move 48 you have some drawing chances because of the extra pawn and because his pawns are a bit vulnerable on light squares -- especially his c4 pawn which allows your bishop to tie his rook to its defense. Your pawns are on dark squares but with less space you're position is more solid and easier to defend. His bishop can't get to your weak pawns. The difference is basically his rook vs your knight, in these situations if the stronger side wants to win he needs to find a way to infiltrate with his rook, if he can't it's a draw. Also I think if black could trade off all (enemy) pawns on one side of the board it would be pretty much drawn as the knight + extra pawn can equalize against a rook when action is confined to one side of the board, the opposite bishops ease this defense.
Besides these general things your knight gets an excellent outpost on e4 and your pieces are very active while his king isn't in the action, so a draw isn't unlikely.
That said white missed a few chances. 53. g5 was a mistake because it allows you to trade off some pawns which is what black wants to do, but it was mostly a mistake because this is one point he can try to infiltrate because the bishop isn't hitting c4 and your king is on the d file. He should play Ra1 with Ra7+ then Ra6 to create a passer. White also missed the same opportunity on moves 54 (you shouldn't have played f5 because again the rook goes to the a file) and move 60 (it was important to put your bishop back on f7). He finally caught on at move 62 that he needed to try this but it was too late and your king was close enough to stop it, at this point it looks like a draw and there isn't a way for white to improve his position. He could try a timely exchange sacrifice RxN at some point, but this just leaves an opposite bishop ending and his king is still out of play.
Just finished this game against a stronger opponent. I'm down the exchange for a pawn. I thought the final stages was interesting, with his King immobilised, and me always able to defend the d pawn, but also to switch over to prevent the Rook from coming in on the a file. I dont believe I could ever get more than a draw, but could my opponent break down my fortress?