The defending champion was set for an early exit when down 4-5 and 15-40 in the deciding third set but leant on his rocket serve to fight back, level the match at 5-5, and then break Ginepri for the first time in the contest in the following game.
Isner then disposed of the world number 281 quickly in his final service game, closing the contest with four straight aces to take his tally to 30 for the night on the Georgia hard court.
"I was a nervous wreck out there but fortunately for me I was able to hit two big serves and bring that game back to deuce and it really turned the match around," the world number 12 told reporters.
"He returns very well, that’s what he does best, and he was giving me fits on my serve tonight.
"I actually served a lot better as the match progressed, and I had to because he was returning well, and that last game, I can’t serve any better than that."
Earlier, lucky loser Thiemo De Bakker of the Netherlands recorded a big upset by beating second seed Kevin Anderson of South Africa in straight sets.
Ranked a distant 142nd in the world, the 25-year-old Dutch right-hander took down the world number 17 6-4 7-5.
"It proves that I can play against (the top players)," De Bakker told reporters.
For Anderson, the runner-up to Isner last year, it was a disappointing night.
"I didn't feel like my normal serve out there," the Florida resident said.
"I felt a step behind the whole match. I thought he played well, hit the ball quite big. I was disappointed with how I played."
Seventh seed Yen-Hsun Lu was also bounced out after losing 6-4 6-3 to Germany’s Benjamin Becker, who set up a quarter-final match up with De Bakker.
Australian Marinko Matosevic, the eighth seed, was too good for American Tim Cmyczek as he won through 6-4 7-5.
The Australian, who won 61 per cent of his service points and converted five of seven break points, faces Isner in the last eight.
(Reporting by Ben Everill in Los Angeles. Editing by Patrick Johnston)
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