Tsonga, a Frenchman seeded No. 12, came back after dropping the first two sets then had to save a match point while serving and trailing 16-15 in the fifth. Tsonga got the only break of the final set -- which alone lasted more than two hours -- to go ahead 18-17.
The final score: 6-7 (3), 3-6, 7-6 (5), 6-2, 19-17 for Tsonga in nearly 4½ hours.
"It's good to be alive," said Tsonga, who won his 103rd Grand Slam match, tying him with Jean Borotra at the top of the list of French players with the most victories in majors.
Tsonga improved to a 15-7 career mark in five-setters, including 6-0 at Wimbledon, while Isner fell to 6-15.
"To be honest, I was a little tired, for some reason," said Isner, who leaned over with hands on knees at one point. "I didn't think I would be."
Isner reiterated his stance that all Grand Slam tournaments should use a tiebreaker to settle a fifth set. Currently, only the US Open does that, while Wimbledon, the French Open and Australian Open make players continue until one winds up with two more games than the other.
"But I can't do anything about it," he said. "It's fine."
Isner and Tsonga played the first three sets at No. 2 Court on Saturday before play was suspended because of darkness.
In the first round of Wimbledon in 2010, Isner beat France's Nicolas Mahut 70-68 in the final set of the longest match in tennis history, which lasted more than 11 hours over three days.
Tsonga faces countryman Richard Gasquet (No. 7) in the fourth round.
Gasquet, a two-time semifinalist at Wimbledon, finished off a 2-6, 7-6 (5), 6-2, 6-3 victory over Albert Ramos-Vinolas on Sunday.
An all-Czech matchup was assured in the fourth round when No. 10 Tomas Berdych and Jiri Vesely both advanced. Berdych, the Wimbledon runner-up in 2010, beat 19-year-old rising German star Alexander Zverev 6-3, 6-4, 4-6, 6-1, while Vesely swept Portugal's Joao Sousa 6-2, 6-2, 7-5.