Federer, the four-time champion seeded seventh, beat French qualifier Pail-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."
In a late match, the top-seeded Nadal rallied to beat Radek Stepanek 2-6, 6-4, 7-5.
"He is not the right player to play against in the first round," Nadal said. "He's not the right player because what you want to find in the first round is rhythm and against him every point is different. He goes quick to the net. They don't give you that few games to find your rhythm, to find a way that you want to play."
Nadal is 41-6 in his 10 appearances here and has made it to the semifinals or better for the past eight years. But he said worries about his back affected his serve during the 2-hour, 24-minute contest.
"With my serve I was doing nothing. When that happens, the opponent is able to play more aggressive, play more confident and in the end, eight double faults, I give him an opportunity to win a lot of free points," Nadal said.
"I was a little bit scared for the back. I am not feeling 100 percent confident with my serve. But probably that match is going to help me understand that I can start to serve normal again."
The fifth-seeded Murray topped Lukas Rosol 4-6, 6-3, 6-2, and the third-seeded Wawrinka, playing for the first time since winning the Australian Open, beat Ivo Karlovic 6-3, 7-5.
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 Na beat Chinese compatriot 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 Wozniack 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."
