Playing in front of his home crowd in the huge Pala Alpitour indoor arena, the world No.4 was streets ahead of his opponent in Sunday's opener even if the score looked reasonably close.
Sinner served superbly throughout and struck his groundstrokes with venom, needing just one service break in each set to wrap up a routine victory.
World No.1 Novak Djokovic was beginning his quest later on Sunday when he was set to face Danish youngster Holger Rune.
Sinner wrapped up the opening set in 40 minutes and when he broke serve at the start of the second set he never looked like relinquishing control against a flat-looking Tsitsipas.
The Italian, who has qualified by right for the season-ender for the first time, sealed victory with an ace.
"It was a long week before coming here and I was excited to finally step on court," the 22-year-old Sinner said. "I knew it would be tough but I think I answered the questions really well.
"It's a special week, such an incredible feeling playing here with the roof closed and the crowd."
Djokovic, bidding for a record seventh title at the event, will seal the year-end World No.1 ranking for an eighth time if he wins just one group match.
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