Harrison, who had 27 aces in his previous match, finished with only five this time but won the final 10 points -- including a 7-0 whitewash in the tiebreaker. The 19-year-old American will play qualifier Dimitar Kutrovsky of Bulgaria in the next round. It will be Harrison's fourth quarterfinal appearance in an ATP event.
Harrison, ranked 94th in the world, got off to a fast start but had to outlast Ginepri in a tight third set.
"He started a little slow," Harrison said. "But in the second set, I had a little mental lapse and he got into a rhythm."
Ginepri, attempting a comeback after missing almost two years following a mountain-bike accident that broke his left elbow, led 5-4 in the third set before Harrison tied it. Ginepri, ranked 235th in the world, went up 6-5 before Harrison took over.
"His ranking is very deceiving right now," Harrison said. "He's a far better player than that."
In the tiebreaker, Harrison whipped a 122 mph ace to close it out.
"I was glad to get it back in the third," Harrison said. "Throughout the tiebreaker, I was able to come up with some good stuff."
A week ago, Harrison won an emotional match that helped the U.S. beat Switzerland in the Davis Cup.
The second-seeded Roddick is playing with a slight tear in his right hamstring sustained during the Australian Open. He also twisted his right ankle Wednesday during his match against Denis Kurda.
Stepanek, from the Czech Republic, is ranked 29th in the world. Darcis is No. 72 and is seeded 22nd in the tournament. It was their first meeting since 2008, when they split two matches.
Fifth-seeded Julien Benneteau of France defeated Gilles Muller of Luxembourg 6-2, 6-4 and will face Darcis in the quarterfinals. It was the first meeting between the two since 2005, when Mueller defeated Benneteau on grass.
Benneteau is ranked 34th in the world, while Muller is 70th.
Sixth-seeded Kevin Anderson of South Africa also advanced to the quarterfinals.
Anderson, ranked 35th in the world, took advantage of two days' rest when he beat a tired Mark Ebden of Australia 6-1, 6-2. Ebden played a match that lasted 2 hours, 30 minutes on Wednesday night to advance to the second round.
Kutrovsky, ranked 435th in the world, beat Blake Strode 7-5, 6-3.
Strode, playing in his first ATP main draw match, was a last-minute substitution for defending champion Gael Monfils, who withdrew from the tournament with an inflamed tendon Wednesday night. The United States-born Strode is ranked 393rd in the world.