Tomic came from a set down to defeat the world number nine 4-6 6-1 6-4 in just under two hours.
Fish made the most of his only break point to take the first set, but he did not get another look in as Tomic took his chances to seal victory.
Former US Open champion Andy Roddick ground out a 7-6 (7/3) 7-5 victory over Bulgaria's Grigor Dimitrov.
The 10th seed's serve was not at its potent best and he was broken once in the first set and twice in the second, but the 29-year-old did enough to close out victory in two hours two minutes.
Nicolas Almagro, the seventh seed, broke once in each set to complete a 7-5 6-3 win over fellow Spaniard Tommy Robredo.
Eighth-seeded Gilles Simon was a more convincing winner, brushing aside Spain's Albert Montanes 6-1 6-1.
Stanislas Wawrinka battled back from losing the first set against American Donald Young, the Swiss 13th seed running out a 6-7 (5/7) 7-6 (7/2) 6-2 winner.
Germany's 15th seed Florian Mayer ended Argentinian wild-card David Nalbandian's hopes with a 6-3 6-4 success.
In the first round, ninth seed Janko Tipsarevic went out, Spain's Feliciano Lopez beating the Serbian 7-6 (7/2) 7-6 (7/3).
Serbia's Viktor Troicki, the 11th seed, crashed out too, losing 6-3 6-3 to American qualifier Ryan Harrison.
Twelfth-seeded Ukrainian Alexandr Dolgopolov and Austrian Jurgen Melzer, the 14th seed, fared better, the former beating Poland's Lukasz Kubot 6-4 7-6 (8/6) and the latter a 6-4 6-2 winner over Croatia's Ivan Ljubicic.
Elsewhere, Spanish qualifier Albert Ramos saw off Croatia's Marin Cilic 6-3 6-4 and Canadian Milos Raonic came from a set down to defeat France's Michael Llodra 6-7 (2/7) 6-2 7-6 (7/5).
Other first-round winners included Radek Stepanek, Alex Bogomolov Jr, Dmitry Tursunov and Kei Nishikori.