Tsonga, who often suffers lapses in concentration, lost his momentum following a 40-minute suspension in play after a side panel from the scoreboard fell on the crowd from the upper part of Court Philippe Chatrier, injuring three fans.
Tsonga, a semi-finalist at Roland Garros in 2013, relied on his booming forehand to unsettle the U.S. Open runner-up, who only got into his groove late in the second set after the interruption.
Tsonga, looking to become the first Frenchman to win his home grand slam since Yannick Noah in 1983, struggled in the third and fourth sets, but was more focussed in the decider.
He will face eighth seed Stan Wawrinka, who knocked out fellow Swiss and second seed Roger Federer, for a place in Sunday's final.
"ROLAND JE T'AIME," Tsonga wrote with his feet on the Paris clay before laying down on his back, his arms outstretched.
"I am super happy it was tough because he came back strong but I kept my head high," Tsonga told reporters.
What looked to be heading for a rapid win turned out to be a massive battle for Tsonga.
The Frenchman raced into a 4-0 lead as Nishikori showed early nerves and he wrapped up the opening set with a forehand winner. He won his fourth game in succession to open a 2-0 lead in the second but another ugly backhand unforced error by Nishikori put the Frenchman 4-1 ahead.
Play was suspended for 40 minutes at 5-2 after the panel fell on to the crowd.
The break helped Nishikori, who claimed a break back, and although Tsonga clinched the set, the momentum had shifted.
Tsonga wasted three break points for 5-4 in the third set and Nishikori seized his opportunity to take the set following a service return blaster.
Looking at the sky, his team in the players' box and talking to himself, the Frenchman looked rattled.
Nishikori piled on the pressure and levelled the match with a flat forehand.
But with his back to the wall, Tsonga found his rhythm again, breaking for 3-1 in the decider when his charge to the net forced Nishikori to send a forehand long and he closed out the set to seal victory.
(Editing by Ed Osmond)
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