Dimitrov posted his first break midway through the second set and controlled the match the rest of the way for a 3-6, 6-4, 6-1 win over the sixth-seeded Benneteau. He dropped serve twice in the first set but wasn't broken after that.
Dimitrov lost just 12 points -- one on serve -- in sweeping through the third set.
The only other seeded player on Tuesday's schedule needed to come from behind to advance. No. 5-seeded Feliciano Lopez got past Adrian Ungur 2-6, 6-4, 7-6 (9-7). Lopez managed just one break on the day but didn't lose his serve after the first set.
Thomaz Bellucci routed Blaz Kavcic 6-1, 6-1, winning two-third of the points in the match. He lost eight total points in his seven games serving.
Also Tuesday, Ernests Gulbis edged Filippo Volandri 7-6 (7-2), 4-6, 6-3; Dustin Brown slipped past Sergiy Stakhovsky 3-6, 6-4, 7-6 (10-8); and Lukasz Kubot beat Ivan Dodig 3-6, 6-3, 6-4. Jan Hajek was up 4-1 in the first set when Edouard Roger-Vasselin retired.
Celebrity Breakups and divorces of 2014 [PHOTOS]