Playing at Key Biscayne for the first time since 2011, Wawrinka beat Daniel Gimeno-Traver of Spain 6-0, 3-6, 6-3 after a first-round bye.
Wawrinka, who won the Australian Open in January, improved to 14-1 this year. His lone defeat came last week in the fourth round at Indian Wells to Kevin Anderson.
Wawrinka has never reached the quarterfinals in five previous appearances at Key Biscayne, but then he has never been ranked this high.
"I'm No. 2 in the world," he said. "I know that if I play my best tennis I can be a favorite of the tournament. I know how well I can play."
Wawrinka hit 33 winners against Gimeno-Traver and shook off some sloppy play midway through the match.
"I was negative in the second set, a little bit stupidly, but then I'm really happy the way I started the third set," Wawrinka said. "First one here, it's never easy. The conditions were really slow today, really humid. You need to get through."
No. 7 Tomas Berdych joined Wawrinka in the third round by beating Stephane Robert of France 7-6 (5), 6-1.
Ana Ivanovic advanced to the fourth round by beating Flavia Pennetta of Italy 6-4, 6-3. Ivanovic improved to 5-1 this year against top-20 players.
Angelique Kerber, seeded No. 5, defeated Tsvetana Pironkova of Bulgaria 6-0, 6-2, and No. 8 Petra Kvitova beat Croatian qualifier Donna Vekic 6-3, 6-4.
Sabine Lisicki of Germany withdrew because of the flu, giving Kirsten Flipkens of Belgium a walkover.