Back from injury, the former world number one lost the first set to Denis Kudla before hitting back to win 6-7 (5/7) 7-6 (7/5) 6-4.
Elsewhere, rising star Ryan Harrison got through his second-round match, coming from behind to beat Olivier Rochus 4-6 6-2 6-3.
The teenager was 3-1 down in the final set, but used his serve to his advantage and turned things around with 27 aces.
Sam Querrey lost his second-round fixture with Denis Istomin, taking the first set but then losing 5-7 6-3 7-5.
Meanwhile, Matthew Ebden defeated Dudi Sela 6-7 (7/9) 6-2 7-6 (7/1) and Julien Benneteau, the fifth seed, saw off Ryan Sweeting 7-6 (7/3) 7-6 (7/5).