Fish recorded a 1-6, 6-1, 6-3 decision over Michael Berrer to set up a second-round meeting with second-seeded Novak Djokovic.
The 32 seeds in the 96-player field received byes past the first round at the annual stop in Indian Wells, Calif.
Carlos Moya survived two tiebreaks to get to the second round, defeating Tim Smyczek 7-6 (9-7), 7-6 (7-5). Moya's second-round opponent will be No. 26 seed Thomaz Bellucci.
Among the other first-round winners were Ramon Delgado, Mario Ancic and Rainer Schuettler.
Roger Federer is the top seed in the tournament. Victor Hanescu and Juan Ignacio Chela will meet Friday for a chance to take on Federer in the second round.
2014: The Year in Music [PHOTOS]