After Novak Djokovic's win over Tomas Berdych earlier on Friday, Murray knew he only needed to take one set off seventh seeded Tsonga to guarantee his third appearance in the last four of the season-ending event.
The 25-year-old took just 33 minutes to achieve his goal and he eventually sealed his second win of the tournament, advancing from Group A in second place behind Djokovic, despite a late flurry from Tsonga.
After a glorious year which has featured his first Grand Slam title at the US Open, a gold medal in the Olympic singles and a first appearance in the Wimbledon final, Murray would love to cap the campaign with a first Tour Finals crown.
To do that he is likely to have to get past defending champion Roger Federer, who will be the Scot's semi-final opponent on Sunday if, as expected, the Wimbledon champion finishes top of Group B.
"It was quite a tough scenario and I was lucky to get off to a good start," Murray said.
"There was some good tennis at the end of the second set. Jo started playing better.
"When he was imposing himself as he was in that second set, he is a hell of an athlete and very tough to play."
Tsonga, beaten in his previous two group matches, required a straight sets victory to sneak through at Murray's expense, but his track record suggested the outcome wouldn't go his way.
Murray had won six of their previous seven clashes, including a semi-final success at Wimbledon earlier this year, while Tsonga had lost all 11 of his meetings with top-eight ranked players this year.
Cleverly mixing the pace and flight of his groundstrokes, Murray quickly took charge and tempted Tsonga into a series of rash shots from the baseline that gifted the Scot a break in the opening game.
Murray continued to baffle Tsonga with his astute shot selection and secured a second break for a 3-0 lead when the frazzled Frenchman drove a forehand into the net.
Tsonga, the Tour Finals runner-up 12 months ago, finally got on the scoreboard when he held serve in the fifth game, but Murray refused to relinquish his strangehold and easily closed out the set.
Murray kept his foot on the gas and broke in the first game of the second set thanks to a Tsonga double-fault.
Yet, with defeat looking certain, Tsonga underlined why he can be so frustrating as he suddenly started playing with real purpose and broke Murray to love to level at 4-4.
Tsonga saved two break points at 5-5 and kept the pressure on Murray, who had to save a set point to force a tie-break.
But the Scot refound his rhythm in the breaker and some searing groundstrokes ended Tsonga's resistance. – Sapa-AFP