Murray, who could do no better than second in Group A after his defeat to Novak Djokovic on Wednesday, needed just one set to secure his place in the last four.
The world number three did the job almost too quickly for the packed indoor arena’s liking, starting with a break, which he backed up and repeated to effectively end the match as a contest within a quarter of an hour in front of a star-studded crowd including the likes of Fabrica Muamba, Kevin Spacey and Peter Schmeichel.
Tsonga, who has been some way short of the form that took him to last year’s final, appeared to concede defeat in a terrible first set, which ended his slim hopes of reaching the semis.
But he was brilliant at times in an exhibition-style second that he took to a tie-break after some thrilling exchanges at the baseline and net, at one point earning set point only to be pegged back by Murray’s forehand.
The shoot-out lived up to its preceding set in terms of quality, with Murray shading it after taking a couple of mini-breaks and acing his way to glory from 6-3, the Scot ultimately possessing too much variety for the Frenchman as he closed out the win in one hour and 36 minutes.
Murray will probably face Roger Federer in the semi-finals, unless the Swiss blows up against Juan Martin Del Potro, while world number eight Tsonga’s season is over.
“It’s quite a tough scenario when you know a straight sets defeat would put him in. It was important to get the first set and the second was better, with some excellent rallies,” Murray said afterwards.
“The second set was down to Jo playing better – he’s a fantastic athlete and he played some great tennis.
“Ivan (Lendl) said to me before the match to forget that I just needed to win one set, but I didn’t listen to him.
“You never know who you’ll play, as Juan and Roger have had some good matches such as the French Open, the Olympics and Juan winning in the final in Basel.”
Murray takes his record against Tsonga to 7-1, and has not lost to him since the 2008 Australian Open.
Tsonga, who is almost as popular in Britain as he is in France, found it hard to explain his lack of form in London this year.
"Maybe I played better tennis last year. I don't know," he mused at a press conference afterwards. "But nobody knows because it is difficult to evaluate the level of every player.
"So maybe this year they were just better than last year, and that's it. Maybe I was at the same level, maybe not, maybe I was better - it's always difficult to say."
Both semis are on Sunday with the final on Monday night in London's Docklands.
3-Andy Murray (Britain) beat 7-Jo-Wilfried Tsonga (France) 6-2 7-6(3)
1-Novak Djokovic (Serbia) beat 5-Tomas Berdych (Czech Republic) 6-2 7-6(6)