Federer had nine aces and no double faults in a 6-4, 6-2 victory. Nieminen managed four break chances but Federer fought them all off while converting three breaks in four opportunities himself.
Federer was particularly sharp in the second set, dropping just five points over four games serving and winning more than half of the points off Nieminen's serve.
No. 2-seeded Kei Nishikori was on the court 61 minutes in disposing of Matthew Ebden 6-2, 6-4. Nishikori didn't face a break point, losing 11 points in nine service games.
Marinko Matosevic earned a quarterfinal slot opposite Federer with a 5-7, 7-6 (7-3), 6-4 win over Sam Querrey and Marin Cilic, behind 16 aces, ousted fifth-seeded Grigor Dimitrov 7-5, 7-5 and will next play Nishikori.