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The Czech fourth seed won 6-3, 7-6 (7/4), grabbing a crucial break against the powerful Frenchman in the eighth game of the first set and edging the second set tie-break to set up a semi-final against Novak Djokovic or Tommy Haas.
"I think it was a really solid game and solid performance from beginning until the end. Yeah, I was feeling quite well on court," said Berdych, who next month is set to be part of the Czech team playing Spain in the Davis Cup final.
"You know, I think the biggest difference between me and Jo was I was able to take the small chances during even the first and especially the second set. It was not many of them, but I was able to keep it and convert it on my side."
Fifth seed Tsonga had early chances to break in the second set but failed to capitalise and Berdych remained unbroken throughout the contest.
With four berths still up for grabs at next month's elite eight-man showpiece in London, Berdych, 27, is sixth in the Race to London while Tsonga, also 27, is in eighth spot.
Berdych said despite a busy end to the season, he would give his all to try to win the Davis Cup for the Czech Republic in Prague.
"Even if there is just a small energy left in my body, I'm going to give it there, leave it there, try my best. Then after that there is the off-season, and I can rest."
World No 1 Roger Federer, Djokovic and Shanghai Masters defending champion Andy Murray have already qualified for London, along with the injured Rafael Nadal.
In the second semi-final on Friday, third seed Murray beat the Czech Republic's Radek Stepanek 4-6, 6-2, 6-3.
In the remaining quarter-finals, Djokovic plays German veteran Haas and Federer goes head-to-head with 10th seed Marin Cilic of Croatia.
Federer's win on Thursday over Davis Cup team-mate Stanislas Wawrinka guaranteed him a record 300th week as world No 1 when the next rankings are published on Monday.
Haas, 34, who reached a best of number two in the world, is one victory away from reaching 500 singles match wins.
Results on the sixth day of the Shanghai Masters on Friday (x denotes seeding):
Quarter-finals
Tomas Berdych (CZE x4) bt Jo-Wilfried Tsonga (FRA x5) 6-3, 7-6 (7/4)
Andy Murray (GBR x3) bt Radek Stepanek (CZE) 4-6, 6-2, 6-3
