Federer came into the tournament on a 12-match winning streak following titles in Basel and Paris, where he beat Tsonga in straight sets in the final a week ago.
The 16-time Grand Slam champion looked set for another easy win when he took the first set in 21 minutes, but Tsonga found his feet and broke early in the second set before taking the match into a decider.
A closely fought third set ended when the pressure seemed to get to Tsonga. Trailing 5-4, he was broken at 15 and Federer chalked up his third straight win over Tsonga since back-to-back losses at Wimbledon and Montreal.
Rafael Nadal was up against Mardy Fish in the second match in Group B later Sunday. Group A begins Monday with Andy Murray facing David Ferrer, and Novak Djokovic against Tomas Berdych.
Nadal, unusually, was courtside to see the end of the Federer-Tsonga match, joining football stars Thierry Henry and Andrey Arshavin in the crowd to watch the opening match of the season-ending tournament for the year's top eight players.
Federer is making his 10th straight appearance, while Tsonga is playing the event for only the second time in his career, and the first time in London.
The gap in experience showed at the start as Tsonga's first serve deserted him in the fourth game, and the Frenchman overhit back-to-back forehands to go 3-1 down.
A tentative half-volley into the bottom of the net by Tsonga gave Federer a second break and the set.
Tsonga began hitting much more freely in the second set and his confidence grew. The 26-year-old drew a huge cheer from the 17,000-strong crowd when he broke for the first time in the third game when Federer sent a forehand wide.
With Federer mistiming his shots much more frequently, Tsonga seized his chance. He broke for a second time to lead 5-2 and then drew another error from Federer to take the set.
Federer went into the third set knowing he had never won a match against Tsonga in a deciding set, and his opponent wasn't showing any sign of wilting.
Federer engineered a break point in the sixth game, but Tsonga saved it with a bold forehand winner into the corner, and celebrated by skipping back to the baseline.
But after a run of three games with only one point against the serve, Tsonga blinked first. His third double fault of the match put him 0-30 down before Federer swept a curving forehand onto the sideline to bring up three match points.
Tsonga delivered a service winner to save the first but on the second, Federer lured his opponent into the net before finishing the match with a pinpoint backhand pass.
