The two-time defending champion delivered his most convincing performance of the week.
"I'm very satisfied by how it went,'' Federer said. "I tried to step up the pressure and so far that's worked well.''
In Saturday's semifinals, Federer faces Feliciano Lopez of Spain, who beat fourth-seeded James Blake of the United States 6-4, 7-6 (7).
Second-seeded David Nalbandian and third-seeded Juan Martin del Potro meet in the other all-Argentine semifinal.
Federer passed up three match points at 5-2 on Bolelli's serve, but served out a love game including two of his eight aces in the match.
Lopez finished the first set against Blake with an ace and, ended his first win against the American with a backhand crosscourt shot.
"This one hurt,'' Blake said. "I had break points in three or four different games. If I expect to beat a lot of the guys out there I need to play well on those points and I didn't do it today.''
Blake said he planned to "get right back on the horse and try to get ready'' for Paris next week in order to qualify for the eight-man Masters Cup in Shanghai.
Nalbandian, the 2002 champion, defeated German qualifier Benjamin Becker 7-6 (4), 6-4, while del Potro beat sixth-seeded Igor Andreev of Russia 6-4, 7-5.
Del Potro beat his Davis Cup teammate for the first time last week in Madrid, and tied their head-to-heads at 1-1.
"Last week I beat him in a great match, and tomorrow I've got to be in good shape if I want to do it again,'' del Potro said.
"My mind is good,'' he added. "I want to keep winning but my physique starts to feel tired. My tennis is going numb.''
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