The world number one is seeking his seventh ATP Tour trophy of the season, and is locked in a battle with Novak Djokovic to finish as the year-end world number one.
Federer won 77 per cent of his service points and converted a late break in the deciding set to claim the second-round contest in two hours and three minutes.
The 31-year-old needs to defend crucial points, having won three consecutive tournaments to finish the 2011 season with a 17-match win streak - Basel, the Paris Masters and the ATP World Tour Finals in London.
Federer will next take on Benoit Paire of France.
In Valencia, Milos Raonic and John Isner were knocked out by lower-ranked opponents, denting their chances of clinching one of two remaining berths at next month's World Tour finals in London.
Eighth-seeded Canadian Raonic lost his first-round match against Luxembourg's Gilles Muller 7-5 7-6, while American Isner, the fifth seed, was beaten 7-6 4-6 6-4 in the second round by Belgian 21-year-old David Goffin, who reached his third Tour quarter-final of the season.
Seventh seed Marin Cilic of Croatia improved his chances of a spot in London when he cruised past unseeded Spaniard Fernando Verdasco 6-1 6-4 in the second round.
Cilic will play Ivan Dodig in the last eight after the Croatian qualifier beat former world number one Lleyton Hewitt of Australia, a wild card at the indoor hard court event, 6-1 3-6 6-2.
Defending champion Marcel Granollers of Spain won his first round match against Czech qualifier Jan Hajek 7-5 6-4.
Top seed David Ferrer plays his second-round match against unseeded Spanish compatriot Albert Ramos on Thursday.
Ferrer, the world number five, has already qualified for London along with Federer, Djokovic, Andy Murray, Rafa Nadal and Tomas Berdych.
ATP Basel results
1-Roger Federer (Switzerland) beat Thomaz Bellucci (Brazil) 6-3 6-7(6) 7-5
3-Richard Gasquet (France) beat Marco Chiudinelli (Switzerland) 6-1 6-4
Grigor Dimitrov (Bulgaria) beat Julien Benneteau (France) 7-6(5) 6-7(1) 7-6(3)
2-Juan Martin Del Potro (Argentina) beat Alejandro Falla (Colombia) 6-4 6-1
Benoit Paire (France) beat 5-Andreas Seppi (Italy) 4-6 6-2 6-3
Marinko Matosevic (Australia) beat 7-Florian Mayer (Germany) 6-2 6-3
Paul-Henri Mathieu (France) beat Henri Laaksonen (Switzerland) 6-2 7-5
ATP Valencia results
7-Marin Cilic (Croatia) beat Fernando Verdasco (Spain) 6-1 6-4
David Goffin (Belgium) beat 5-John Isner (U.S.) 7-6(2) 4-6 6-4
Ivan Dodig (Croatia) beat Lleyton Hewitt (Australia) 6-1 3-6 6-2
Gilles Muller (Luxembourg) beat 8-Milos Raonic (Canada) 7-5 7-6(1)
Marcel Granollers (Spain) beat Jan Hajek (Czech Republic) 7-5 6-4
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