Murray raced into a 3-0 lead in the decider, but Tsonga fought back with two quick breaks to transform the match.
And although he surrendered a 40-0 advantage when serving for the match at 5-4, the Frenchman held on to book his spot in the last four.
"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," said Murray.
"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."
Victory capped an impressive 48 hours for Tsonga, who deposed of world number one Novak Djokovic on Thursday in the third round.
The world number 15 will next face either Grigor Dimitrov or Kevin Anderson.
Results from the Toronto Masters Men's Singles Quarterfinal matches on Friday
13-Jo-Wilfried Tsonga (France) beat 8-Andy Murray (Britain) 7-6(5) 4-6 6-4
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