The Scot lost a tight opening set on a tie-break and appeared set to bow out at the quarter-final stage when he offered up two break points at 4-4 in the second.
He hung tough to save his serve, though, and then broke the Frenchman - conqueror of Novak Djokovic on Thursday - before charging into a 3-0 lead in the decider.
But he inexplicably crumbled, losing five games in a row before slumping to a 7-6 (7/5), 4-6, 6-4 loss.
He was visibly frustrated as his chances disappeared in front of him, though Tsonga deserved immense credit for his fightback.
The see-saw nature of the second and third sets was entirely out of keeping with the opener, which Tsonga won on a tie-break after 12 consecutive holds of serve. He got ahead in the breaker when Murray hit a forehand long.
The pair traded breaks early in the second set and Murray then looked set for straight-sets exit when he offered up two more break points. He found a way to save them, however, and then broke himself before winning the set with a hold to love.
He carried that confidence into the decider and was soon 3-0 ahead as Tsonga got erratic, before the tables turned dramatically.
"I had to play around my return position quite a lot, and I started to get into more service games in the second and third set," Murray said.
"I thought it was a high-level match with a few games by both of us in the second and third sets that were a bit scrappy. Jo is a top player. He's a fantastic athlete. When his game is on, he's very tough to beat."
In the women's event, held in Montreal, world No.1 Serena Williams' title defence picked up speed in a 4-6, 7-5, 7-5 quarter-final win over Caroline Wozniacki to set up a semi-final showdown with sister Venus.
Serena, who won the title last year in Toronto, is back in Montreal for the first time in 14 years, while Venus is making her first visit to the belle province, but it could be a memorable one.
After seeing off 14th seeded Spaniard Carla Suarez Navarro 4-6, 6-2, 6-3 last night, the American now faces a 25th meeting against her sister and a first since a 2013 semi-final encounter in Charleston, which was won by Serena.
Both Serena Williams and Wozniacki arrived in Montreal in winning form. Williams, a three-time champion on the Canadian hard courts, picked up her 61st career title last week at Stanford while Wozniacki was champion in Istanbul. Neither had dropped a set on route to the quarter-finals.
The match served up plenty of intrigue, with Williams going against an ex-world No.1 and former- champion, who has her own love affair with the Montreal hard courts where she had built a 9-1 record.
The muscular American had little hope of outworking Wozniacki, who is training to run the New York City marathon in November, but Williams had enough weapons and experience to see off the dangerous Dane.
In the opening set, Wozniacki had one break point and made it count, while Williams could not convert either of her two opportunities.
Wozniacki again took the initiative in the second, breaking the 17-time grand slam winner at the first opportunity, but Williams would not throw in the towel, sweeping three straight games to surge in front 5-4 and then break the Dane to close out the set.
After trading a pair of breaks to start the third it was Williams who delivered the knockout blow, with one last break to clinch the match.