Defending champion Jelena Jankovic also advanced with a 6-3, 7-6 (6) win over Argentina's Gisela Dulko in a match suspended for about 3 1/2 hours due to rain, and French Open champion Ana Ivanovic defeated Italy's Francesca Schiavone 6-3, 6-4.
Safina lost her serve in the opening game and allowed her 35th-ranked opponent to take the initiative for most of the first set.
But the 23-year-old Russian dominated the tiebreaker and then kept the momentum with an early break in the second set before winning the last four games. She closed out the match in 1 hour, 50 minutes.
"I was a little bit tight,'' Safina said. "Winning the first set gave me confidence. ... I just started to play a little bit better in the second set.''
Safina, a runner-up here in 2006, is looking for her first title since ascending to the top of the world ranking on April 20. She complained that the rain before the match had made the court damp and dangerous to play on.
"I was just so angry, because you can get injured,'' said the Russian, who fell in the first set as she rushed to the net to retrieve a drop shot, but couldn't slide. "It's soft and you're afraid to play.''
She said tournament organizers should "have a little bit respect to us as the players.''
Jankovic has won the Italian Open for the past two years, but the 24-year-old Serb was far from her best against the 39th-ranked Dulko.
Jankovic won early breaks in both sets but let her opponent break back both times. She saved four set points when down 5-4 in the second, before rain forced the suspension at 5-5.
After play resumed, the third-seeded Jankovic squandered four match points in the tiebreaker before taking the set and the match.
"I had everything under control, and all of a sudden, she's on top of me and she has set points to win the second set,'' Jankovic said. "It was difficult, but I managed to somehow stay positive and stay strong and win that second set.''
The top eight seeds all had first-round byes in this warmup for the French Open, which begins May 24. Second-ranked Serena Williams was scheduled to play later Tuesday.
After finishing the 2008 season as No. 1, Jankovic went through a slump at the start of this year and has dropped to No. 4. She won her first title of the year in Marbella, Spain, last month, but was upset by Italy's Flavia Pennetta in the quarterfinals in Stuttgart, Germany, last week.
The fifth-seeded Ivanovic is also looking to regain her top form. She started off strong against Schiavone, closing the first set in 39 minutes and taking control of the second with a break to love in the ninth game that let her serve out the match.
In other matches, No.7 Svetlana Kuznetsova of Russia beat Daniela Hantuchova of Slovakia 6-3, 6-3, and eighth-seeded Nadia Petrova of Russia beat Carla Suarez Navarro of Spain 6-2, 3-6, 6-3.
No. 9 Caroline Wozniacki of Denmark, 12th-seeded Flavia Pennetta of Italy and No. 16 Kaia Kanepi also advanced, while 11th-seeded Marion Bartoli and fellow Frenchwoman Alize Cornet were both upset.
The 13th-seeded Cornet lost 6-4, 6-1 to Kateryna Bondarenko of Ukraine, and Maria Jose Martinez Sanchez of Spain beat Bartoli 6-1, 7-5.
