"He just played good tennis", admitted Tsonga, who suffered an embarrassing first-round exit against Renzo Olivo at the French Open.
Tsonga was only one of four remaining seeds in the draw after Andy Murray, Milos Raonic and Stan Wawrinka all were knocked out on Day 2, with Nick Kyrgios pulling out midway through his match with Donald Young on the opening day.
2014 champion Dimitrov fired 15 aces, won 87 percent of his first serve points and saved five of Benneteau's six break point chances.
"Sometimes you can not do anything because the guy in front of you is doing the right things to make you play in a bad way", Tsonga said.
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"I don't look at those things", Dimitrov said, "not when you look at all the players who are lower ranked but can beat anyone, as we saw yesterday".
Benneteau paid the price for not converting his break point try early on in the decider as Dimitrov went on to break the French in the fifth game and never looked back to seal the win. He also saved five of six break points to move into the quarterfinals, where he will play either Daniil Medvedev or Thanasi Kokkinakis, the victor against Raonic.
Seventh seed Tomas Berdych tamed Canadian teenager Denis Shapovalov to move into the last eight with a 7-6 (7/4), 6-7 (4/7), 7-5 victory.
"This young kid is the future", Berdych said of Shapovalov, whose whipped forehand and kicking serve out wide were entertaining features of his game.
American Donald Young also progressed, beating Serbia's Viktor Troicki in straight sets 6-3 6-4.