Djokovic is the seventh seed in TurinFormer world number one Novak Djokovic beat second seed Stefanos Tsitsipas in two tight sets in his opening match of the ATP Finals in Turin.
The 35-year-old Serb overcame Tsitsipas of Greece 6-4 7-6 (7-4).
Djokovic is seeking to equal Roger Federer's record of six victories in the season-ending tournament.
Earlier in the same group, Russian Andrey Rublev came from a set down to beat compatriot Daniil Medvedev 6-7 (7-9) 6-3 7-6 (9-7).
Rublev, seeded sixth, held his nerve in a final-set tie-break to overcome the fourth seed after squandering seven set points in the opening set.
On Sunday, Rafael Nadal's latest bid to finally land the first ATP Finals title of his career started with a defeat by American eighth seed Taylor Fritz.
Top seed Nadal will face Canadian Felix Auger Aliassime in his second Green Group round-robin match on Tuesday.
The Turin tournament sees eight of the year's best men's players split into two groups of four, with the top two qualifying for the semi-finals.
Meanwhile, Great Britain's Neal Skupski and Dutch partner Wes Koolhof won their first men's doubles match 7-6 (7-3) 4-6 10-5 against Australian duo Nick Kyrgios and Thanasi Kokkinakis.
The pair have enjoyed incredible success in their first year together, winning seven titles which have included Masters 1000 victories in Madrid, Montreal and Paris, and finishing 2022 as year-end world number ones.
Former world number one Joe Salisbury, seeded second with American Rajeev Ram, will face fellow Brit Lloyd Glasspool and his Finnish partner Harri Heliovaara on Tuesday.
ATP Tour Finals: Which player has the best statistics of 2022?
