Fish's presence in the draw was notable, as he has played infrequently since withdrawing on health grounds ahead of a scheduled fourth-round match with Roger Federer at last year's US Open.
The 31-year-old former top-10 player has had to contend with heart issues which have disrupted his career, and he had played only two tournaments this season before this week, the most recent a low-profile Challenger in April.
Fish was up a set but down a break in the second when his first-round match against Russell was called off due to rain on Tuesday night. The match continued to turn against him when they resumed in Wednesday evening's night session and Russell beat the two-time former Atlanta champion 4-6 6-2 7-5.
Russell said on the ATP website: "I played fantastic. Mardy's such a great competitor. I thought he played really well, first match back in four months. I thought it was a really high quality match. Both of us, on big points, were coming up with great shots. It's a positive for both of us going into the summer."
Australian seventh seed Lleyton Hewitt ousted American Rhyne Williams after a tough battle, the former US Open and Wimbledon champion winning through their second-round tussle 7-6 (8/6) 6-4.
Croatian third seed Ivan Dodig also survived a stiff test, edging past Lithuanian Ricardas Berankis 6-1 6-7 (3/7) 6-3 to set up a clash with Hewitt in the quarter-finals.
The first-round action was completed as Americans Christian Harrison and James Blake reached the last 16, along with Australian Matthew Ebden who had taken the first set 6-2 in his tussle with Ivo Karlovic when the Croatian retired, citing fatigue.