Fish, the former world number seven who is down at 64 in the rankings after a heart problem restricted his playing schedule this year, came through 2-6 6-1 6-3.
"I still feel a little uneasy and that's to be expected. It's not all going to be roses right away," he said.
"These will be the sort of situations I have to get through to be 100 per cent. These sort of post-traumatic experiences are what I have to get over.
"A lot of it is mental. A little bit is physical."
Fish will take on 12th-seeded Frenchman Julien Benneteau in the second round.
Also on Monday, Australian qualifier Samuel Groth blasted 20 aces to beat American Denis Kudla 7-6 (7/2) 6-2 and book a second-round match against Canadian fourth seed Milos Raonic.
Groth's compatriot Marinko Matosevic ousted veteran American James Blake, 6-2 7-6 (8/6).
"The first set, I really served poorly, and he took advantage," Blake said. "The second set, I fought back and had a chance. I didn't make my shots when I needed to."