Trailing 5-4 in the third set, the 12th-ranked Isner fought off two match points and evened it at 5-5 with consecutive aces.
The former University of Georgia star had 30 aces overall. He had his only service break of the match before firing four straight aces to close out Ginepri, an Atlanta resident ranked 281st.
Earlier,Thiemo de Bakker pulled off the upset that Ginepri could not when the Dutch qualifier beat second-seeded Kevin Anderson of South Africa 6-4, 7-5 in a rain-delayed match to advance to the quarterfinals.
De Bakker retired from his final qualifying match because of a sore neck yet made the field as one of three "Lucky Losers" following the late withdrawals of Gaels Monfils, Richard Gasquet and Radek Stepanek.
Isner staved off a bigger upset bid than Anderson faced.
He needed a second-set tiebreaker win to outlast Ginepri, a 31-year-old, part-time pro whose only ATP or Grand Slam win of the year in five matches came when he beat Sergiy Stakhovsky 7-6 (3), 3-6, 6-0 in the first round.
Isner won the tiebreaker 7-5 with an ace to push his career tiebreaker winning percentage to 64.55 percent, second-best in tennis history to Roger Federer's 64.8.