advanced by beating Tomas Berdych 6-2, 7-6 (6).
Because Djokovic won the early match at the O2 Arena in straight sets, Murray needed only to win one set to ensure his passage.
However, he said he was unsure about what would get him through when he took the court, adding that coach Ivan Lendl just told him to focus on winning and not worry about just winning one set.
"I didn't know exactly what I needed to do. But obviously when he said that, I kind of realized," Murray said.
"Then I just asked the umpire at the change of ends after the first set whether I was through or not. Then he said I was. That was it."
He won that set easily, too, breaking Tsonga's serve in the first and third games en route to a 4-0 lead.
Murray had another early break in the second set, but Tsonga got it back to even the score at 3-3 and eventually force the tiebreaker.
"I'm somebody who never gives up," said Tsonga, who lost all three of his matches. "So sometimes ... you not playing a good tennis, and you keep fighting, you keep believ(ing) in you, and then it comes better and better, and that's it."
Murray (2-1) finished second in Group A, while Djokovic (3-0) was first.
The ATP finals is the last tournament of the season, and only for the top eight players in the world.
In Group B, six-time champion Roger Federer has already qualified for the semifinals and will face Juan Martin del Potro in his final group match on Saturday.
David Ferrer is also in the group and can still qualify for the semifinals, but Janko Tipsarevic has been eliminated.
If Federer wins his group, he would face Murray in the semifinals.
"I think over the years, I got used to playing those guys a couple of times in a week or whatever," said Murray, who lost to Djokovic in the group stage. "It's not something that I'm afraid of. I know it's incredibly difficult and challenging to beat guys like that back-to-back, but it's doable."
Before coming to London, Djokovic lost in the second round of the Paris Masters, and said after that match that he felt down physically.
But against Berdych, the top-ranked Serb ran all over the court, retrieving ball after ball and making his opponent work hard on nearly every point.
"If you are winning matches, I mean, obviously you feel better," Djokovic said. "But still, I mean, the fact is that it being the last tournament of the year here in London for most of the players."