But compatriot Laura Robson lost 6-4 3-6 7-6 (7-4) to Taiwan's Chang Kai-Chen
Watson needed just under two hours to see off Parmentier, who was ultimately unable to resist a barrage of baseline returns from the Channel Islander.
Parmentier had to face a whopping 18 break points, losing seven of them while only managing to take three games off the 20-year-old's serve.
Watson is now guaranteed to move into the top 60, and could well end the week ahead of Robson - who is all-but guaranteed a top-50 place now - if she goes on to win the tournament.
Robson, who has reached a career-high 54 after a runner-up showing in Guangzhou, a semi-final appearance in Palermo and a run to the fourth round at the US Open, went down in 119 minutes to her 134th ranked opponent.
The eighth seed failed to seize on her opportunities as Chang saved nine out of 11 break points before winning the tense tie-breaker. She will meet Australian top seed Samantha Stosur who beat American Jamie Hampton 6-2 6-4.
Watson faces Japan's Misaki Doi for a place in the final after the home favourite stunned seventh seed Chanelle Scheepers of South Africa 2-6 6-1 6-3.
- Laura Robson