The top-ranked Federer saved four consecutive set points in the second-set tiebreaker before the 34th-ranked Bellucci tied the second-round match.
It was not until match point that Federer, who held serve throughout, had the decisive break-point chance in the decider.
Federer will face either Benoit Paire of France or Lukasz Kubot of Poland in the final eight Friday.
Paire beat fifth-seeded Andreas Seppi of Italy, 4-6, 6-2, 6-3 in a first-round match.
Also advancing to the quarterfinals was third-seeded Richard Gasquet of France who beat Federer's boyhood friend Marco Chiudinelli, 6-1, 6-4. Grigor Dimitrov of Bulgaria had 17 aces in defeating France's Julien Benneteau 7-6 (5), 6-7 (1), 7-6 (3).
In other first-round action, second-seeded Juan Martin del Potro of Argentina eased past Alejandro Falla of Colombia 6-4, 6-1; Marinko Matosevic of Australia upset seventh-seeded Florian Mayer of Germany 6-2, 6-3; and France's Paul-Henri Mathieu beat Henri Laaksonen of Switzerland 6-2, 7-5.
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