Fish had played only two tournament matches all year before entering the Atlanta tournament. He has been suffering from complications arising from an irregular heartbeat, a condition that has threatened to end his career.
The Russell-Fish match began Tuesday but was suspended in the second set by the second of two rain delays. Russell finally finished off a 4-6, 6-2, 7-5 victory that set up a second-round match with Santiago Giraldo.
Earlier in the day Lleyton Hewitt and Ivan Dodig became the first players to reach the quarterfinals.
Hewitt eliminated Rhyne Williams 7-6 (8-6), 6-4 and Dodig survived against Ricardas Berankis 6-1, 6-7 (3-7), 6-3. Hewitt and Dodig will meet in the quarters.
Other first-round matches saw Christian Harrison oust Alejandro Falla 6-1, 6-7 (7-9), 6-2, James Blake fight off Tim Smyczek 7-6 (7-3), 4-6, 7-6 (7-4) and Matthew Ebden advance when Ivo Karlovic retired in the second set.