Djokovic was in great form as usual, beating eighth seed Matteo Berrettini 6-2 6-1.
Djokovic know has the opportunity to replace Rafael Nadal as world number 1 this week in London
Swiss, Roger Federer plays Dominic Thiem in the same group later on Sunday at the season-ending championships.
The event at the O2 Arena features the top eight players of the year who are split into two groups.
The group stage is a round-robin format with the top two players progressing to the semi-finals with the final held next Sunday.
Nadal is in Group Andre Agassi but is an injury doubt for the tournament with a stomach muscle issue, although the Spaniard said on Friday he is confident of playing against Alexander Zverev in his opener on Monday.