Still, the American played Djokovic on even terms for more than an hour. Ginepri held serve easily until the final game of the first set, when he was broken.
Djokovic blew an easy forehand putaway to lose his serve for the first time, and Ginepri broke again while dominating the second set.
But then Ginepri faded fast, perhaps weary after playing 13 grinding sets in his first three matches. His groundstrokes became more erratic, and Djokovic won five consecutive games and 10 of 11 to take control.
The Serb volleyed well, found the range with his serve and used his drop shot to keep Ginepri off balance. A two-time semifinalist at Roland Garros, Djokovic is bidding for his second major title.
"I played really good in the third and fourth sets," Djokovic said. "I had some really good matches on clay recently. Now I'm in the quarterfinals and I need to keep playing aggressively."
Ginepri, a former top-15 player from Kennesaw, Ga., fell to 0-15 against opponents ranked in the top three.
Roger Federer's goal in the quarterfinals will be to get familiar foil Robin Soderling moving, because the tactic has worked in the past. Federer takes a 12-0 record against Soderling into their match Tuesday, and that includes victories at three Grand Slam events last year.
Federer won when they met in last year's final at Roland Garros, and also beat Soderling in the fourth round at Wimbledon and in the quarterfinals at the U.S. Open.
"We have experience playing against each other," Federer said. "I've never lost against him, so obviously that's a good record to have."
Soderling upset Rafael Nadal in the fourth round at Roland Garros last year, clearing the path for Federer to complete a career Grand Slam. Federer has a funny way of showing any gratitude — he has lost only one of the past 10 sets against Soderling.
What's the key against the big-swinging Swede?
"Any hard hitter, I want to try to get him to move," Federer said. "If they play aggressive off the return and they serve well, then you play more like a hard-court match, which I don't mind doing. Maybe that's why I'm good on many surfaces, because I can adapt to any sort of an opponent."
Federer adapted Sunday to playing good friend Stanislas Wawrinka in a Grand Slam for the first time. They teamed to win a gold medal in doubles at the 2008 Olympics but were on opposite sides of the net in the fourth round, and Federer won 6-4, 7-6 (5), 6-2.
Soderling advanced by beating No. 10 Marin Cilic 6-4, 6-4, 6-2.
Another match Tuesday will feature two first-time Roland Garros quarterfinalists, No. 11 Mikhail Youzhny and No. 15 Tomas Berdych. Youzhny advanced when No. 8 Jo-Wilfried Tsonga retired with a right hip injury trailing 6-2, and Berdych defeated No. 4 Andy Murray 6-2, 7-5, 6-3.
Two women's quarterfinals matchups are set: No. 5 Elena Dementieva will play No. 19 Nadia Petrova, and No. 3 Caroline Wozniacki will face No. 17 Francesca Schiavone.
Petrova advanced by beating No. 2 Venus Williams, 6-4, 6-3. Williams came into the tournament with the best record this year on the women's tour, but she's 0 for 14 trying for a French Open title.
Four-time champion Justine Henin advanced to the fourth round when she rallied in a winner-take-all set, beating Maria Sharapova 6-2, 3-6, 6-3. The match had been suspended overnight after two sets.