The Frenchman went ahead in the fourth game due largely to a series of unlucky breaks for Tipsarevic.
The Serb pushed a forehand long after a gust of wind caused the ball to dip viciously as it went onto his racquet, before a net cord sent the ball wide on break point.
Benneteau held his nerve to serve out the first set to take the lead.
Tipsarevic worked his way into the match, grinding for every point. That forced Benneteau into a few costly errors.
The eighth seed's hard work paid off as he levelled the score at a set apiece.
However, Benneteau quickly regrouped in the third set, dominating with his serve - landing 73% in and taking 74% of the points on his first serve.
He sealed the set 6-2, but the match took yet another swing in the fourth, as Tipsarevic clinched it 6-4 to take the match into a decider.
The Serbian's youth began to tell, and his legs were evidently fresher than his opponent's.
Benneteau began to make more lazy errors upon which Tipsarevic gratefully capitalised.
After breaking at the first time of asking, Tipsarevic was looking well on course for victory. He brought up three match points on the Frenchman's serve at 5-2.
The 31-year-old then staged a rousing comeback to hold and force Tipsarevic - now looking a bit tight - to serve out for a place in the fourth round.
The 28-year-old needed another two match points before eventually sealing a clash with Nicolas Almagro.