Tomic was 4-1 up in the second set, but Stepanek fought right back and despite facing two break points when serving for the match at 6-5 up, he managed to stay cool and closed it out.
Next up for Stepanek will be the 5th seed David Ferrer of Spain, who had a first round bye.
Also through to the second round is the Croatian Marin Cilic, who defeated Spanish wild card holder Albert Montanes in straight sets 6-3 6-3.
With this win, Cilic equaled the head to head record against the Spaniard to 1-1 and after reaching the BMW Open final in Munich last week, he looks all fired up.
Cilic will play 8th seed American John Isner in round 2.
In the other first round matches, Argentine qualifier Federico Delbonic beat the Spaniard Albert Ramos 6-3 6-2, 9th seed Gilles Simon of France overcame Italy’s Fabio Fognini 6-7 (1) 6-3 6-3 and 16th seed Alexandr Dolgopolov of Ukraine eliminated Pablo Andujar of Spain 7-6 (5) 6-4.