Both players struggled to hold serve throughout their match on Court Two, with former world number one Halep breaking her Belgian opponent six times.
The Romanian, who won the title in 2019, has slipped to 18th in the world rankings.
Defeat marks the end of 36-year-old Flipkens's singles career.
The players embraced at the net and Flipkens, a semi-finalist in 2013, kissed the court.
Halep will play Poland's Magdalena Frech in the last 32.
