Roger Federer, the 2009 men's champion, was another player kept waiting by the weather and although the Swiss did get on court, he walked off in the gathering gloom unsure about his last eight prospects, locked at one-set all with Gael Monfils.
After home favourite Alize Cornet's run petered out in a bitter 6-2 7-6(9) defeat by Ukraine's 19th seed Elina Svitolina in a match held up for three hours by the rain, home eyes turned to Tsonga on Court Philippe Chatrier.
All seemed to be going well when the local favourite led by two sets against bad-tempered Czech fourth seed Berdych, who seemed unhappy to be playing in on-and-off drizzle, but when he served for the match at 5-4 in the third the dampness seemed to get into his circuitry and he fluffed his chance.
Berdych pounced to take the third set on a tiebreak and, as French cheers from fans huddled under colourful umbrellas in the stands turned to near silence, the Czech moved a break ahead in the fourth and looked favourite to go on and win.
Out of nowhere, however, the spring returned to Tsonga's step and with an onslaught of heavy hitting he reeled off five games in a row to win 6-3 6-2 6-7(5) 6-3.
The injury-plagued Tsonga sealed victory when Berdych wafted a backhand long and the Frenchman danced for joy before conducting the crowd's "Oles" with his towel.
It was only the third time in nine meetings that 30-year-old Tsonga, seeded 14, had beaten Berdych and his reward is a quarter-final against Japan's Kei Nishikori.
Title tip Nishikori had not struck a ball in anger since his second-round win over Brazil's Thomaz Bellucci on Wednesday after his third-round opponent Benjamin Becker of Germany pulled out with an injury.
If there was any rust, however, he soon shook it off to outclass Russian Teymuraz Gabashvili 6-3 6-4 6-2 and reach the quarter-finals at Roland Garros for the first time.
He also became the first Japanese man to get this far at the French Open for more than 80 years and he sounded like he had no intention of stopping yet.
"I think quarter-final that's the first goal for this week," the 2014 U.S. Open runner-up said. "I hope it's just the start of my journey, and I hope I can keep going."
Eighth seed Stan Wawrinka made up for lost time as he blew away Frenchman Gilles Simon 6-1 6-4 6-2 to set up a last eight encounter with either fellow Swiss Federer or Monfils.
MATCHES POSTPONED
Two of the scheduled women's fourth-round matches were postponed -- Sharapova's clash against Czech 13th seed Lucie Safarova and Italian Flavia Pennetta's meeting with Spain's Garbine Muguruza.
Those matches will be wedged into Monday's schedule when better weather is expected in the French capital.
French number one Cornet's first appearance in the last 16 of her home grand slam got off to a terrible start as she went 5-0 down to Svitolina in the first set before the rain arrived.
She fought tooth and nail after that but her 20-year-old opponent was too far ahead. Although Cornet saved five match points and dragged the second set into a tiebreak, she was unable to continue her quest.
The home hope was left seething after a tight call went against her on break point down at 5-5 in the second set -- the umpire climbing off the chair to confirm Svitolina's claim that Cornet's shot had landed fractions long.
"It's a scandal," Cornet told a news conference. "It's shameful. I don't know how she could look me straight in the eye and tell me the ball was out."
Svitolina will next face former champion and world number one Ana Ivanovic after the Serbian seventh seed beat Russian Ekaterina Makarova 7-5 3-6 6-1.
Ivanovic will be appearing in the quarter-finals at Roland Garros for the first time since winning the title in 2008.
(Reporting by Martyn Herman and Julien Pretot; Editing by Mark Meadows and Ken Ferris)
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