Djokovic has a chance to overtake Nadal for the year-end No. 1 ranking with a strong showing in London.
The 32-year-old Djokovic began the match 640 points behind Rafael Nadal in the race to end the year on top of the rankings, but victory chipped that advantage down to 440.
The second-seed Serb, who has been drawn in the Bjorn Borg Group, needed just 64 minutes to beat his less experienced opponent.
The first four games were shared on serve but Djokovic seized the opening break when Berrettini missed a routine forehand at 2-3 and quickly took charge.
Djokovic romped into a 4-0 lead in the second set as the Italian continued to struggle with his serve but was pegged back in the fifth game as Berrettini broke for the first time.
"It feels great to be back", said the Wimbledon champion. "It was not easy for him to be playing his first Tour Finals match and I knew he might be a bit nervous".
But the unflappable 16-time Grand Slam champion broke immediately and completed victory with a routine forehand victor off his own serve to take the set 6-1.
Germany's Alexander Zverev shocked Djokovic in last year's final at the O2 Arena but the Serbian is the firm favourite to equal Roger Federer's tally of six ATP Finals titles after cantering to victory at last week's Paris Masters.
Federer, bidding to win a record seventh title at the season-ending event, takes on Austrian Dominic Thiem in the evening match.
The season-ending tournament, featuring the year's best eight players, is contested in a round-robin format with the best four players and doubles teams reaching the knockout semi-finals stage.
Nadal, Daniil Medvedev, Stefanos Tsitsipas and Zverev are in the Andre Agassi group.