The 62-minute victory sent the Swiss top seed into a Friday clash with Frenchman Julien Benneteau who he will be facing for the sixth time.
World number two Federer is playing in Rotterdam for the eighth time and has never gone out before the quarters, winning titles in 2005 and 2012.
"I'm happy, the conditions are very quick and Thiemo is a dangerous opponent," said Federer.
"I'm glad to go through and be in the quarter-finals again," he said.
"It was a good win."
Second seed Juan Martin Del Potro said he's not envious of the world top four as the big Argentine beat qualifier Ernests Gulbis 7-6 (7/5), 6-3.
"I know that I can improve," said the seventh-ranked 2009 US Open champion, who next faces Jarkko Nieminen after the Finn dispatched German qualifier Matthias Bachinger 6-3, 5-7, 6-3.
"But the top four are there for a reason, they are playing better than me, I know that I can beat them, but I need to improve my level"
Del Potro, who lost the final a year ago to Federer, needed just over 90 minutes to beat Latvia's Gulbis, who once stood inside the top 30 before falling to his current 132.
Marcos Baghdatis handed Frenchman Richard Gasquet only his second loss of the season as the Cypriot scored a 6-4, 6-4 win to reach the quarter-finals.
Gasquet lined up in Rotterdam as the fourth seed, having already won two tour titles this season and boasting an unbeaten record apart from a defeat to compatriot Jo-Wilfried Tsonga at the Australian Open.
But the world number 10 never got going against Baghdatis, who had also beaten him at the Olympics last year.
Baghdatis won in 76 minutes, with nine aces and two breaks of serve, and will now face Bulgarian Grigor Dimitrov on Friday.
Frenchman Julien Benneteau sent defending champion Roger Federer crashing out of the Rotterdam World Tennis tournament on Friday with a stunning 6-3, 7-5 quarter-final upset.
Federer, who lifted the trophy in his last two appearances in 2005 and 2012, last suffered defeat in the event against Tim Henman in 2004.
"I'm very disappointed, I have some regrets about this match," said Federer, who came back from two sets to love down to beat Benneteau in the third round of Wimbledon last year.