Federer, the four-time champion seeded seventh, beat French qualifier Paul-Henri Mathieu. The Swiss star was coming off his 78th career title last week in Dubai.
"It's important to win," he said. "It's a lot different from Dubai. You have to force a bit more, but I'm satisfied."
The fifth-seeded Murray regrouped to top Lukas Rosol 4-6, 6-3, 6-2. The third-seeded Wawrinka, playing for the first time since winning the Australian Open, was a 6-3, 7-5 winner over Ivo Karlovic.
Kevin Anderson and Tommy Haas also moved into the third round. Anderson spoiled two-time tournament champion Lleyton Hewitt's bid for his 600th career match win, topping the Australian 7-6 (5), 6-4. Haas, who will be 36 on April 3, rolled to a 6-3, 6-4 victory over Jeremy Chardy.
In women's play, top-seeded woman Li Na beat countrywoman Zheng Jie 6-1, 7-5, and fourth-seeded Maria Sharapova opened her title defense with a 6-1, 6-4 victory over Julia Goerges. Fifth-seeded Angelique Kerber dropped out, falling 2-6, 7-6 (5), 6-4 to Maria-Teresa Torro-Flor. Aleksandra Wozniak also beat No. 15 Sabine Lisicki 7-5, 1-6, 7-6 (5).
Murray reached the final in 2009, but has mostly struggled in the event.
"I think it's important sometimes to think about it, because when you're not expecting it to happen and then it does, that's when it can kind of take you by surprise and you might panic a little bit or worry," Murray said. "But I don't feel like (that happened) today. I was a set and a break down. I got broken three times in a row the end of the first set, beginning of the second. I just kind of kept going and found a way to win, which is always the most important thing."
Mikhail Youzhny, seeded 14th, withdrew because of a back injury and the American men's contingent was trimmed from its initial 14 members to one after losses by Michael Russell, Sam Querrey, Tim Smyczek and Ryan Harrison. The only U.S. player remaining is 12th seed John Isner, who will face Nikolay Davydenko on Sunday.
Li is playing her second event since winning the Australian Open.
"This is the first match after Doha, two weeks, and of course for I cannot be 100 percent for the first match," Li said. "But I was happy. At least I can learn something from today's match."
Li will face Karolina Pliskova, a 7-5, 6-2 winner over No. 28 Klara Zakopalova.