Second seed Murray, the 2013 champion at the All England Club, goes on to face Czech 10th seed Tomas Berdych on Friday in what will be his 20th semi-final at the majors.
It was 29-year-old Murray's 13th win in 15 match-ups with 12th seeded Tsonga and his 100th career grass court win.
But like Roger Federer, who came back from two sets down to beat Marin Cilic earlier in the day on Centre Court, Murray did it the hard way.
Murray rallied impressively in the decider, screaming out to his box 'there's no way I'm losing this match' before making good on his rallying call.
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"It was a tough match. Tsonga is one of the best grass-court players in the world and he came up with some great shots at big moments," Murray said.
"I just tried to use all my energy at the start of the fifth set to get myself pumped up and thankfully I got the early break and managed to hang onto it."
"At the beginning you try to work your way through and play good tennis but now you are trying to get through matches and play as well as possible and I am happy to get into the semis."
Murray's first problem of the quarter-final was to get grit out of his right eye.
It wasn't too much of a distraction as he broke for 3-2 before Tsonga returned the favour for 4-4.
Both men wasted three set points apiece in the ensuing tie-break before Murray pocketed it, just about fair reward for his high-speed scrambling.
Murray ranted with himself and umpire Fergus Murphy as he went completely off the boil and Tsonga levelled an increasingly tense quarter-final.
But buoyed by his own passionate war cry, Murray raced to a 5-0 lead in the decider before sealing victory with a 15th ace after four hours of breathless ups and downs.
"The the finish line was far tonight," said Tsonga.
"I came back strong in the third and fourth, but I didn't play well in the fifth. Andy was a little better than me on this last set."
But they have never played on grass.
"It will be a very tough match (against Berdych). He has been to the final here, beaten Djokovic and Federer at Wimbledon and is very very good," said Murray.
"He has won some tough matches here, he's played a lot of tennis and I will need to play well.