Halep survived a break point in the opening game before powering her way to a 5-0 lead with two breaks of her own as Rybarikova struggled on serve and committed 19 unforced errors en route to conceding the first set.
The 28-year-old Slovakian conceded the match early in the second set after a medical timeout, giving Halep an opportunity to avenge her U.S. Open first-round defeat by Sharapova.
The Russian, who has never lost to Halep in seven previous meetings, beat compatriot Ekaterina Makarova 6-4 4-6 6-1 to record a second consecutive three-set victory in Beijing earlier on Tuesday.
”You can take a little bit away from all the matches we’ve played in the past,“ Sharapova said. ”We know each other’s games very well. They’ve always been very challenging, tough, competitive, emotional.
“I love the challenge of playing against someone that’s number two in the world. She’s a great player. She’s had a great year.”
Twice grand slam champion Petra Kvitova dominated American qualifier Varvara Lepchenko in a battle of left-handers, the Czech winning 88 percent of points on serve to progress to the third round with a routine 6-4 6-4 victory.
Kvitova faces fifth seed Carolina Wozniacki next, in what promises to add another intriguing chapter to their eight-year rivalry.
Number 12 seed Kvitova holds a 6-5 lead in her head-to-head record with Wozniacki, having won their last two matches in straight sets.
Fourth seed Karolina Pliskova hit nine aces as she edged out German qualifier Andrea Petkovic 6-4 6-4 to set up a clash with Sorana Cirstea of Romania.
American CoCo Vandeweghe was forced to retire early in the second set against Daria Gavrilova, sending the Australian through to face Czech Barbora Strycova, while China’s Duan Ying-ying lost to Russia’s Elena Vesnina.