The number two seed started the match in confident fashion and took the attack to the American's serve, putting her under pressure immediately. The Romanian got the breakthrough and earned another to allow her to seal the first set 6-2.
It did not take long for Halep to break again as Rogers lost her composure to allow the 23-year-old an early advantage. Halep continued to dominate on the court and had the chance to serve out for the match, but was broken by the American.
However, Halep secured her victory in the next game by breaking the serve of Rogers yet again to seal her place in the last 16.
Halep will face either Sabine Lisicki in the fourth round of the competition.