Serbian Djokovic, who beat Federer in last year's final, must win at least two of his Group B matches to have any chance of toppling Rafael Nadal who opened his Group A challenge with an easy victory over David Ferrer earlier in the day.
World number seven Federer, bidding for a seventh title at the year-ender, fired a forehand wide to give Djokovic the opening set after 37 minutes of an eagerly-awaited contest in front of a sell-out crowd at the 02 Arena.
The 17-times grand-slam champion produced some vintage play in the second set but squandered a set point at 5-4 as the crowd willed the 32-year-old to go the distance.
They got their wish as Federer dominated the tiebreak against an opponent looking weary under the lights.
Just when Federer appeared to have given himself a fighting chance of an increasingly rare victory over one of the big guns, however, Djokovic slammed the door in his face.
The Serbian broke the Federer serve to love at the start of the third set and then fought off a break point to open up a two-game lead he never looked like relinquishing.
Another break condemned Federer to his first opening-match defeat at the Tour Finals since 2008 when he failed to survive the group stage and defeat by Frenchman Richard Gasquet on Thursday would leave him staring at a similar fate.
Djokovic, whose winning now spans 18 matches since he lost to Nadal in the U.S. Open final, joins Argentine Juan Martin del Potro, whom he plays on Thursday, at the top of the group.