Serena was making her first appearance since January
Serena Williams defeated Timea Bacsinszky in straight sets to win her first match since January at the Italian Open on her return from injury.
American Williams, the world number one, defeated her Swiss opponent 7-6 6-1 to progress to the third round.
But Dinara Safina, who was making her return from a career-threatening back injury, was beaten in straight sets on Tuesday in Rome.
The Russian number three seed lost 6-4 6-7 6-1 to Alexandra Dulgheru.
Safina admitted following her match that she was well short of match practice, following her injury lay-off.
"I was too out of touch with the racket. I had only practised a little bit so this was disappointing," said Safina.
"The only good thing out of this match is that my back was fine."
Elsewhere Venus Williams saw off Patty Schnyder in straight sets to win her first match in a month.
The American, seeded fourth, dropped her first service game in each set but recovered to win 6-2 6-2.
Venus has been sidelined with a knee injury since losing the final in Key Biscayne to Kim Clijsters in March.
"I'm feeling pretty good," she said. "I took some time off and I started hitting some balls a couple of weeks ago. I've been doing a lot of fitness."
For sister Serena it was her first match since winning the Australian Open on 30 January.
The American came through a tough first set which went to a tie break before her class told, easing through the second to set up a clash with German Andrea Petkovic in the next round.
"I had been spending a lot of time on court,'" admitted Serena. "My body is fine. It's feeling better. When you first come back, you're never really 100%.
"At first you just have to start playing some tournaments to see how it goes."
Serena won her fifth Australia Open title after a hard-fought, three-set win over old rival Justine Henin. She indicated that the knee was also bothering her in the warm-up tournament in Melbourne.
"After Australia, I was amazed even how I was able to win the tournament," she said. "I had to totally recover from that whole Australia bonanza."
In other matches, second seed Caroline Wozniacki took just 50 minutes to claim a 6-1 6-0 win over Maria Elena Camerin.
Former world number one Ana Ivanovic, who has slipped to 58 in the world rankings, showed signs of a return to form as she beat ninth seed Victoria Azarenka 6-4 6-4.
Serbia number seven seed Jelena Jankovic also came through her second round clash, defeating American qualifier Bethanie Mattek-Sands 6-3 3-6 6-1.
Russia's Elena Dementieva, seeded sixth, went through 6-4 7-5 against Yaroslava Shvedova, while Polish eighth seed Agnieszka Radwanska was a 6-1 6-0 winner against Roberta Vinci.
Fellow seeds Yanina Wickmayer, Nadia Petrova and Shahar Peer all progressed, but Italians Flavia Pennetta and Francesca Schiavone, seeded 12th and 13th respectively, both crashed out in straight sets.