After a slow start, Williams hit 29 winners and erased six of the seven break points she faced as she defeated Monica Niculescu, 6-3, 6-1, in her opening match at Key Biscayne, Fla.
"It was a little sore in practice, but it was OK today," Williams said of her knee.
Venus Williams defeated Samantha Stosur, 6-4, 7-6 (3), and will next play Caroline Wozniacki.
Four-time champion Novak Djokovic wobbled badly midway through his opening match but regrouped to beat Martin Klizan, 6-0, 5-7, 6-1.
Djokovic, seeded No. 1, was on the verge of an easy victory when he served at 5-3 in the second set. But he was broken and lost serve again two games later.
"I felt under pressure the last couple of games of the second set. I got a little bit tight," Djokovic said. "But in the third I managed to bounce back."
Djokovic had 19 break-point chances and converted only seven, but still improved to 20-2 this year.
No. 11-seeded Jo-Wilfried Tsonga made a successful 2015 debut by beating American Tim Smyczek, 6-4, 3-6, 6-3. Tsonga sat out the start of this year with a right arm injury.
"I didn't expect to play my best tennis today," Tsonga said. "But it's normal when you didn't play a couple of months. I hope it's going to be better and better."
American John Isner beat 17-year-old wild card Andrey Rublev of Russia, 6-3, 6-4. Rublev is the world's No. 1-ranked junior.
"I needed to come out ready to play," Isner said, "because he's a very talented kid. Anything can happen."
Another American, Jack Sock, eliminated No. 21 Fabio Fognini, 7-6 (4), 6-1. No. 5 Milos Raonic and No. 6 David Ferrer also advanced to the third round.