Berrettini was making his debut at the event for world's top eight players and had never faced Djokovic before.
Roger Federer's pursuit of a seventh ATP Finals title got off to a poor start on Sunday when the Swiss great lost 7-5 7-5 to Austrian Dominic Thiem in his opening group match.
The Swiss 20-time Grand Slam victor recovered quickly from being broken in the first game of the match but the Austrian fifth seed repeated the dose in the 11th game and took the opening set 7-5.
Berrettini's forehand was responsible for 18 of those errors, including two shots into the net to hand Djokovic the only two breaks of the first set.
Djokovic, jostling with Rafael Nadal to finish the year as world number one, swept aside O2 debutant Matteo Berrettini 6-2 6-1 in a shade over an hour. The only time Federer has failed to progress to the knockout stages was in 2008.
Djokovic has a chance to overtake Nadal for the year-end No. 1 ranking with a strong showing in London.
The second-seed Serb, who has been drawn in the Bjorn Borg Group, needed just 64 minutes to beat his less experienced opponent.
Thiem served and returned superbly, improving his record against Federer to five victories and two defeats as he bids to end a fruitful 2019 by claiming a sixth title of the year.
Earlier in the day Djokovic thrashed Matteo Berrettini 6-2, 6-1 so he will take on Thiem on Tuesday.
"There's no other reasonable explanation (to that reaction) than trying to play as flawless as possible", Djokovic said from London.
"Over the years I've played really well in this arena".
"It was not easy for him at his first Finals match, I knew he would be nervous at the beginning and I used my experience to perform well". The 33-year-old said he was happy to be in London after being forced to pull out of last week's Paris Masters at the semi-final stage with an abdominal strain, but admitted he was not serving at full tilt ahead of his opening match against defending champion Alexander Zverev.
The Serbian, who has won 16 majors and is chasing the end-of-year number one ranking, said he had twisted "Roger, Roger" chants into Novak chants in his mind at Wimbledon.
Nadal, Daniil Medvedev, Stefanos Tsitsipas and Zverev are in the Andre Agassi group.