America's Isner, ranked 12th in the world, was playing his first match of the tournament after enjoying a first-round bye, and nearly fell at the first hurdle.
Ginepri had Isner on the ropes with a 5-4 lead in the third set, but Isner used his big serve to save two match points and level the set at 5-5.
He broke Ginepri in the next game and went on to claim a 4-6, 7-6 (7/5), 7-5 victory.
The 142nd-ranked De Bakker converted three of his 13 break chances against world number 17 Anderson to gain the victory in the rain-disrupted match.
"I felt a step behind the whole match," said Anderson. "I thought (De Bakker) played well, hit the ball quite big. I was disappointed with how I played today."
De Bakker, who delivered his fourth ace of the contest on match point, said the victory proved he can play against the game's top players.
"My goal is to play them more and more often and also to improve my level of play," he said.
In the quarter-finals, De Bakker will play Germany's Benjamin Becker, who ousted seventh-seeded Lu Yen-Hsun 6-4, 6-3.
Isner next faces eighth-seeded Australian Marinko Matosevic, who reached his fifth quarter-final of 2014 when he defeated American Tim Smyczek 6-4, 7-5 in 95 minutes, breaking Smyczek five times.
The other two quarter-finals were set on Wednesday. Fourth-seeded Vasek Pospisil of Canada will play Israel's Dudi Sela and American Jack Sock will take on Slovakian Lukas Lacko.
- Sports & Recreation
- John Isner
- Robby Ginepri
- Thiemo De Bakker