The Swiss player needed just 52 minutes to overcome Falla, and will play Philipp Kohlschreiber in the last eight after the German's 6-4, 7-5 victory over Federer's countryman Marco Chiudinelli.
Germany's Benjamin Becker, world ranked 52nd, caused an upset when he knocked out the second-seeded Nikolay Davydenko of Russia 6-3, 6-4.
Becker, who next faces compatriot Mischa Zverev, ensured there are five Germans in the last eight.
Zverev, ranked 145 in the world, had earlier conquered sixth-seeded Jurgen Melzer of Austria, the French Open semifinalist, 3-6, 7-6 (2), 7-6 (3).
Federer, a five-time winner of the grass-court event in Halle, conceded just two break points in his second-round match on center court but saved both of them.
"I think I controlled the game and dominated at times," he said.
"The result does not lie, to be honest. I was able to vary things well, play cleverly and I knew I would have chances on his serve, and I took them."
Federer has not dropped a set against Falla from three meetings, and the statistic did not look under threat on Thursday.
"It was not much of a battle, but you still have to concentrate a lot and make sure you vary things," Federer said.
"It is more a matter of keeping your concentration than anything tactical or technical."
Federer feels more will be required in the quarterfinal against Kohlschreiber, the home favorite.
"It's definitely going to be a tough game," said world No. 2 Federer.
"I know the strength of Philipp. He has not really shone a lot here yet, but the important thing is to go through.
"On grass, anybody has a chance. It was easy today, but whenever it gets to 2-2, 3-3, 4-4 or 5-5, it is not so easy to get through. He knows that and I know that."
Federer also knows he cannot rely on the usual support he receives on center court at the Gerry Weber Stadion.
"The spectators are fair and respectful with every player, but they will support the German player and I expect the fans to be about 60 percent for Philipp," he said.
Kohlschreiber is aware of the size of his challenge.
"He is certainly the best grass-court player, and I am going to have to put him under pressure, but that is easier said than done," Kohlschreiber said.
"I have just got to ensure I have a good day, then who knows?"