Top seed Williams needed just 30 minutes to begin her bid for a first calendar Grand Slam as Vitalia Diatchenko retired at 6-2 2-0 down.
Nadal, seeded eighth, saw off 18-year-old Borna Coric 6-3 6-2 4-6 6-4. World number one Novak Djokovic went through, but fourth seed Kei Nishikori was beaten.
The Japanese player, last year's runner-up, lost 6-4 3-6 4-6 7-6 (8-6) 6-4 to Frenchman Benoit Paire.
"It's always very sad to lose in the first round, but I think he was playing good tennis so I don't think I played bad," Nishikori said.
Djokovic swept past Brazil's Joao Souza 6-1 6-1 6-1 to reach round two, and Nadal showed glimpses of his best form in beating Croatia's Coric.
The Spaniard, 29, dominated the first two sets and then saw off a resurgent Coric in the fourth with a rasping forehand to earn the decisive break.
"I think I started playing well," Nadal said. "The first two sets was a very high level for me, then I got a little bit tired.
"The conditions here are very humid, I am sweating a lot and in those conditions I suffer a bit. I was able to play aggressive in the fourth. He is an amazing player and has a great future."
There were several upsets in the women's draw, where Serbian seventh seed Ana Ivanovic was beaten 6-3 3-6 6-3 by Dominika Cibulkova of Slovakia, and she was followed out of the tournament by five more seeds.
Serena Williams was generous in her praise for 25-year-old Russian Diatchenko after a workout that last just 37 points, with the American winning 32.
"I told her I was proud of her for coming out and making this effort, knowing she was injured," Williams said. "That's a great effort."
Five seeds in Serena Williams' half of the draw lost on the opening day
Her chances of reaching the women's final were boosted even before the world number one began her title defence as seeds tumbled to leave the American with no other top-10 player in her half of the draw.
As well as Ivanovic, eighth seed Karolina Pliskova - who lost 6-2 6-1 to Anna Tatishvili - and 10th seed Carla Suarez Navarro failed to progress, while world number three Maria Sharapova withdrew on the eve of the tournament because of injury.
Former champion Svetlana Kuznetsova, seeded 30th, and former finalist Jelena Jankovic, seeded 21st, also exited on day one.
Williams' sister Venus, the two-time champion, did advance to the second round, beating Monica Puig - only her second victory since losing in the last 16 at Wimbledon.
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