Russian Zverev, a two-time winner at the year-ending tournament, put on a powerful display to see off world number two Alcaraz who is not on top form after returning from injury at the end of last month.
Wimbledon champion Alcaraz struggled with lower back and left foot problems which had kept him out of action since the Shanghai Masters in early October.
He was then dumped out early at the Paris Masters by Russian qualifier Roman Safiullin (26) and flagged towards the end of a bruising contest with giant German Zverev, the number seven seed in Turin.
Zverev is tough opposition on hard courts like the one at the Pala Alpitour and made full use of his height and power to see off Alcaraz and take the lead in the Red Group.
Before Zverev's win, Novak Djokovic (36) was presented with the trophy for finishing the season as world number one, a position he secured after winning his thrilling Green Group opener with Holger Rune (20) on Sunday night, a match which lasted more than three hours.
Djokovic is the red-hot favourite to claim his seventh Finals title which would put him out of his own as the record winner, one ahead of retired great and old rival Roger Federer.
"It's obviously the crown of the season, finishing the year as number one in the world I think is a dream of every tennis player, it's one of the most difficult things to do in our sport," said Djokovic on court.
"Winning Grand Slams and being number one in the world are probably the pinnacles of the sport. It's been a very long year for all the players and to be able to stand here is a blessing."
Later on Monday 2020 champion Daniil Medvedev (27) faces fellow Russian Andrey Rublev (25) in the day's other Red Group match.
