The Swiss top seed, playing his second match since his shock second-round exit at Wimbledon, needed just over an hour to seal a 6-4, 6-3 win over 29-year-old Jan Hajek of the Czech Republic.
The 31-year-old Federer, with his world ranking down at five, his lowest for a decade, is playing in Germany with a larger 98 square-inch frame – eight inches bigger than his previous racquets.
“I guess it’s to a degree some more getting use to, just to see how it reacts on every single shot,” Federer said.
“Clearly it reacts better to some shots. But it’s important not to think of it the whole time, not to talk about it all the time, but more just sort of go with it, fight for every point, have the right mindset, be optimistic about playing here now and wanting to achieve a good result and that’s what I’m doing.”
Federer, who faces Germany’s Florian Mayer in Friday’s quarter-final, squandered 10 of his 13 break points against Hajek, including five match points in the eighth game of the second set, but prevailed in 72 minutes.
Having brushed off his Wimbledon cobwebs by fighting back after losing the first set to Germany’s Daniel Brand in Wednesday’s second round, Federer fired down seven aces to Hajek’s two.
Federer has a 31-4 event record in Hamburg, where he won the title in 2002, 2004-05 and 2007 and finished runner-up in 2008 to Rafael Nadal.
“I’m just still looking for the timing and the rhythm here, but the longer I stay in the tournament the more confident I am that I’m going to play better,” he said.
Second-seed Tommy Haas also booked his place in the last eight with a 6-2, 6-4 victory over Argentina’s Carlos Berlocq.
The 35-year-old German is bidding to win his hometown title for the first time in 11 appearances.
In the quarter-finals Haas faces 12th-seeded Italian Fabio Fognini, who dismissed Marcel Granollers 6-2, 6-4 in 90 minutes.
The 26-year-old Fognini won his first tour title in Stuttgart last week, where he beat Haas in the quarter-finals.
“After his tournament success in Stuttgart, he’s currently playing the best tennis of his life,” Haas said of Fognini after the German was critical of his own performance against Berlocq.
“I’ll have to be fully focused.”