The 17-times grand slam champion cruised to a 6-3 6-1 victory over the Serbian world number nine, taking his haul of victims in the event to 40, one more than Ivan Lendl.
Federer, who has won the title a record six times including the last two editions at London's O2 Arena, seized the initiative when he broke Tipsarevic's first service game and never looked like loosening his grip in a one-sided contest.
Tipsarevic, who pulled out of his match at the Paris Masters last week because of illness, qualified for the eight-man tournament as a result of Rafa Nadal's continuing injury woes.
He never looked like recording a first career victory over the Swiss, however, and despite offering dogged resistance there was an air of predictability about the contest.
Federer pounced again to break for a 2-1 lead in the second set and galloped away to victory in little more than an hour.
Group B action continues later on Tuesday when Spain's David Ferrer takes on Argentina's Juan Martin del Potro.
In Group A, world number one Novak Djokovic and U.S. Open champion Andy Murray won their opening matches on Monday.
The top two players from each group go through to Sunday's semi-finals.