Romanian Halep was forced to save four break points in her opening service game for 1-1 but then went on to claim 12 consecutive games to avenge her Indian Wells loss to eventual champion Osaka in March.
The 20-year-old Osaka failed to convert any of her six break-point opportunities before conceding the match in just under an hour.
“I just tried to build my points, to build a little bit of space and open the court, and tried to make winners,” Halep said.
“It’s tough to make winners on this court, for me, but it’s good when I can build the point. I just want to play like today.”
Halep will next meet American Madison Keys, who clinched a 7-6(2) 7-6(0) win over Croatian qualifier Donna Vekic.
Second seed Caroline Wozniacki began her campaign with a comfortable 6-1 6-4 victory over Belgian Alison van Uytvanck.
The 27-year-old Dane, chasing her first claycourt title since 2011, will face 15th seed Anastasija Sevastova for a place in the quarter-finals.
A decade after they last met in Rome, Maria Sharapova once again did enough to secure a victory over Dominika Cibulkova in three sets.
Former world number one Sharapova struck 41 winners as she rallied back from a set down to edge her Slovakian opponent 3-6 6-4 6-2 in a thrilling 2-1/2 hour contest.
