Benneteau, the No. 29 seed, seemed on the verge of pulling off the second huge upset in 24 hours. World No. 100 Lukas Rosol stunned second-seeded Rafael Nadal in five sets late Thursday.
But Federer fought back, surviving a fourth-set tiebreaker and controlling the fifth set to advance 4-6, 6-7 (3-7), 6-2, 7-6 (8-6), 6-1.
Benneteau used a late first-set break to take the advantage and came back from a break down for the 2-0 sets lead. But Federer charged back with a strong third set and took the final two points of the seesaw fourth-set tiebreaker.
The fifth set was all Federer, as he took 26 of the 37 points and finishing off both break chances.
Awaiting Federer in Monday's fourth-round is unseeded Xavier Malisse, who took out 17th-seeded Fernando Verdasco 1-6, 7-6 (7-5), 6-1, 4-6, 6-3.
More to form earlier in the day, defending champion Novak Djokovic moved into the fourth round at Wimbledon with a four-set victory Friday.
Djokovic saw some opportunities slide by in the first set but controlled the match the rest of the way for a 4-6, 6-2, 6-2, 6-2 win over Radek Stepanek. Djokovic won 75 percent of the points on serve after the first set.
By late in the fourth set Stepanek was playing for honor and survived a very long game to cut the deficit to 1-4. But Djokovic came back with three consecutive aces and a fourth serve that Stepanek couldn't handle to hold serve in about 1 minute.
After going 0-for-5 in break chances in the first set, Djokovic finished with seven breaks on the day.
Djokovic will next go against Serb countryman Viktor Troicki, who ousted 15th-seeded Juan Monaco 7-5, 7-5, 6-3 in his third-round match Friday. His six breaks -- two in each set -- were twice as many as Monaco managed.
Djokovic owns an 11-match winning streak versus Troicki.
No. 26th-seeded Mikhail Youzhny eliminated another of Djokovic's countrymen, beating eighth-seeded Janko Tipsarevic 6-3, 6-4, 3-6, 6-3 to set up a fourth-round match against Denis Istomin. Istomin took out Alejandro Falla 6-3, 6-4, 3-6, 7-6 (7-5).
Richard Gasquet, the No. 18 seed, pulled off a minor upset by beating 12th-seeded Nicolas Almagro 6-3, 6-4, 6-4. Opposite him in the next round will be No. 31-seed Florian Mayer, who edged qualifier Jerzy Janowicz 7-6 (7-5), 3-6, 2-6, 6-3, 7-5.
Sam Querrey knocked out 21st-seeded Milos Raonic 6-7 (3-7), 7-6 (9-7), 7-6 (8-6), 6-4 in a second-round match that carried over from Thursday. Querrey dropped serve just once across the 3-hour match. His break in the fourth set allowed him to advance to the third round against 16th-seeded Marin Cilic.