Federer, this year's second seed and the 2009 champion, earned a 6-2, 7-6 (7-1), 6-3 triumph over Spain's Marcel Granollers, while the eighth-seeded Wawrinka notched a 6-3, 6-4, 5-7, 6-3 victory over Serbia's Dusan Lajovic.
There wasn't much drama for Federer, although he did have to battle back from a deficit in the second set. Granollers broke serve for a 4-2 lead, but Federer broke right back and dominated the eventual tiebreak.
Wawrinka recovered from a minor hiccup in the third set and squandered three match points in the fourth before finally finishing off Lajovic with a break of serve. He will next face surprising American Steve Johnson, who followed his upset of Spain's Guillermo Garcia-Lopez in the first round with a four-set win over Sergiy Stakhovsky on Wednesday.
Japan's Kei Nishikori also moved on in straight sets Wednesday. The fifth seed eased past Brazil's Thomaz Bellucci, 7-5, 6-4, 6-4. Bellucci was coming off a win last week at the French Open tune-up in Geneva.
Another early winner Wednesday was 12th-seeded Frenchman Gilles Simon, who eliminated Slovakia's Martin Klizan in three sets.