Williams, 28, surrendered a few early service breaks but steadied herself with precise play from the backcourt to defeat Estonia's Kaia Kanepi 7-5, 6-4.
The younger of the Williams sisters kept the pressure on Kanepi, eventually forcing the 24-year-old to send a sliced backhand into the net to end the first set.
The pair stayed on serve for most of the second set, but Williams sealed the win when she broke the 48th-ranked Kanepi for the fifth time in the final game.
Safina, looking to bounce back after an embarrassing loss last week in Japan to a teenage Taiwanese qualifier, defeated Italy's Roberta Vinci 6-4, 6-4, but it was not as straightforward as the score suggested.
The pair traded breaks throughout the match, with Safina losing her serve four times and the 26-year-old Vinci surrendering hers six times.
"There is still room for improvement in my game," Safina told reporters.
"She's not an easy one to play... you have to really pick the right shot to go for it. She has a great touch."
The 23-year-old Safina will face Chinese wild card Zhang Shuai in the second round, while Williams will take on Russia's Ekaterina Makarova.
Svetlana Kuznetsova, the tournament's sixth seed and reigning French Open champion, survived a scare from China's Zheng Jie, falling behind early in both sets but outlasting her opponent 7-6 (7/3), 7-5.
The 24-year-old Russian -- who is ranked sixth in the world but also crashed out early in Tokyo -- was on the ropes in the first set against world number 32 Zheng, losing her first service game and quickly falling behind 0-3.
But Kuznetsova, who won the China Open in 2006, rallied with powerful ground stroke winners to pull even at 3-3 and Zheng, clearly the crowd favourite, came up short in the first set tiebreak, surrendering the set on an unforced error.
The 26-year-old Chengdu native, who had never beaten Kuznetsova in four previous meetings, again went up early in the second set, but the Russian showed perseverance to close out the match in straight sets.
"I think that I started both sets pretty slow. I wasn't quite moving well," Kuznetsova said after the match.
"Then when I started to move better, I started to play better. Then I lost my concentration again, and then got it back and started to play better."
Russia's Elena Dementieva, the fourth seed, and number five Caroline Wozniacki of Denmark were due on court later Sunday.
Third seed Venus Williams of the United States advanced to the second round on Saturday.
In other first round matches on Sunday, Russian seventh seed Vera Zvonareva beat Romania's Sorana Cirstea 6-2, 6-2, and Switzerland's Patty Schnyder got past Poland's Urszula Radwanska 6-4, 7-5.
Ninth seed Victoria Azarenka of Belarus advanced, easily defeating compatriot Olga Govortsova 6-1, 6-3.
The men's main draw gets under way on Monday, with Rafael Nadal, Novak Djokovic and Andy Roddick leading the charge.