The 2006 champion rallied from a 5-3 deficit in the tiebreaker with some excellent shotmaking, including a backhand that landed in the far corner on match point.
"(I'm) happy to be back on tour,'' Federer said. "Happy with this first round. it was always going to be tough against Radek and he played a great second set.''
Federer, playing his first ATP event since winning the U.S. Open last month, will next face Australian Open finalist Jo-Wilfried Tsonga.
"I'm excited. He's had a rocky season with injuries this year, so I feel for the guy,'' Federer said of his French opponent. "He's probably one of the guys you want to be playing out there.''
Novak Djokovic advanced after Victor Hanescu retired due to an apparent groin injury while trailing 6-7 (8), 7-6 (8), 3-1.
"It's a big relief to win ... this is a big boost up for upcoming matches,'' Djokovic said. "He used his biggest weapon which was his serve. (And) I couldn't find any rhythm in return, so he used that wisely.''
Hanescu's aggressive play had Djokovic scrambling, especially when the 1.98-meter (6-foot-6) Romanian followed up powerful serves with swift forehand winners. But Djokovic finally evened the match on his second set point with a crisp backhand passing shot.
Top-ranked Rafael Nadal pulled out of doubles with Carlos Moya on Tuesday due to a slight upper leg injury.
"Every match is important, including doubles, but I've got priorities,'' said Nadal, who next faces Richard Gasquet of France in singles Thursday. "You can't win everything.''
American qualifier Robby Ginepri had the biggest upset of the day, beating fifth-ranked Nikolay Davydenko 4-6, 6-4, 6-4.
Davydenko had 35 winners to 15 for Ginepri, but committed 53 unforced errors over the final two sets. The 63rd-ranked American clinched it when the Russian double-faulted.
Sixth-ranked David Ferrer soon followed Davydenko out of the tournament after losing to Feliciano Lopez 6-4, 7-6 (4) in an all-Spanish match.
Andy Roddick had little trouble getting past Spain's Tommy Robredo 6-3, 6-4.
The eighth-ranked American's booming serve was never seriously challenged by Robredo and Roddick used a break in each set to secure the win.
David Nalbandian won his sixth straight match by defeating Tomas Berdych of the Czech Republic 6-2, 6-7 (5), 6-1.
"Last week I was playing really good, so I came here with confidence and I also like to play here,'' said Nalbandian, coming off a victory at the Stockholm Open. "I'm thinking one game at a time, step-by-step.''
Nalbandian next plays Davis Cup teammate Juan Martin del Potro, who advanced after Jarkko Nieminen of Finland retired when trailing 6-2, 4-2.
Tsonga advanced after rallying to beat Spanish qualifier Marcel Granollers 3-6, 6-3, 7-6 (5).
Federer, who pulled out of the Stockholm Open last week due to fatigue, had only played one singles match since the U.S. Open - for Switzerland in the Davis Cup three weeks ago.
Gael Monfils also advanced after eliminating 2006 finalist Fernando Gonzalez of Chile 6,3, 6-4, and Stanislas Wawrinka of Switzerland rallied to beat Philipp Kohlschreiber of Germany 3-6, 7-5, 7-6 (5).
De La Red: Sanctions Will Not Affect This Saturday
Fish advances to 2nd round at Madrid Masters
