The Italian laid down a marker in the first match of the ATP's season-ending showpiece event in front of a delighted home crowd in Italy's northeast.
Despite trailing his opponent 5-2 in their head-to-head record, Sinner got into an early lead in the first set when he broke at 2-2 and then never looked back as he confidently saw out victory in one hour 25 minutes.
The encounter stayed on serve until the fifth game of the first set, when the fourth seed sprang to break the Greek's serve, needing only one break point to move into the lead he would never relinquish.
Tsitsipas applied pressure on the Italian's serve in the very next game, forcing it to deuce, but Sinner held on to consolidate the break, before serving out the first set to claim it 6-4.
First on serve again in the second set, the Greek world number six was immediately behind the match when Sinner broke his service to lead 1-0, with Tsitsipas struggling to live with the speed of the Italian's groundstrokes.
At 2-0, Sinner forced three break points, but was unable to convert as Tsitsipas doggedly stayed in the match.
Playing on home turf and now a set and a break up, Sinner relaxed into the second ATP Finals event of his career and never looked troubled on his serve as he methodically ticked off the games to claim a straight-sets victory.
The second match of the Green Group in the round-robin stage takes place later on Sunday when first seed Novak Djokovic takes on Denmark's Holger Rune.
Djokovic can seal the year-ending number one spot with a single win in the Finals.
