The Swiss star, seeded second after Novak Djokovic's withdrawal because of a knee injury, hit forehand winners, exquisite drop shots and lobs on the run.
"Clearly a good start for me into the clay-court season," Federer said. "I was able to do all the things I was hoping to. I was consistent; consistently dangerous, too."
He outplayed Kohlschreiber from the start, breaking his serve to begin both sets and wrapping up the win in only 50 minutes. Kohlschreiber's dejected body language showed he knew it was all but over after only a few games.
In other matches, Ivan Ljubicic also reached the third round after defeating Jo-Wilfried Tsonga of France 7-6 (2), 6-4, while big-serving Milos Raonic downed Ernests Gulbis 6-4, 7-5. Tomas Berdych defeated Olivier Rochus 6-2, 6-3 to set up a match against Ljubicic.
"He's clearly the overwhelming favorite for this tournament, even though I haven't seen him play yet," Federer said. "Look, we all know how good Rafa is on this surface. He rarely struggles against guys out of the top 20."
Federer had Kohlschreiber scampering helplessly around center court with a mixture of shots that were beyond his reach.
"I managed to vary the game well and not make too many mistakes," said Federer, whose only title this year is from the Qatar Open in January.
The 16-time Grand Slam champion broke Kohlschreiber twice in each set, saved the only break point he faced with an ace and sealed the victory with his fifth ace of the match to improve to 6-0 against him.
Federer, who trained with Kohlschreiber last summer, has only lost one set to him -- in a tiebreaK at Wimbledon two years ago.
"I think he can play a lot better than he did today," Federer said. "Sometimes there are opponents it works really well against. Others, you realize you have to work the point differently. I know how good Philipp is and how heavy his ball actually is. I was actually quite surprised I was having no problems with his serve."
Djokovic, who is undefeated this year at 24-0, is resting a sore knee. The Australian Open winner defeated Nadal on April 3 to win the title in Miami.
Tsonga is playing without a coach since splitting from Eric Winogradsky.
"I am very disappointed," Tsonga said. "I had the feeling I was playing extremely well for a set and a half."
The 20-year-old Raonic was relieved to get through after squandering three straight match points when leading 5-4 in the second set.
"I don't think I've ever done that before," he said. "I think I just played a sloppy first one, then after that just nerves got a bit in the way."