World number two Zverev ensured he would advance after taking the first set 7-6 (7/5) after more than an hour of battle in northern Italy and then swept through the second for his third victory in as many matches.
Alcaraz, who won at Wimbledon and Roland Garros this season but has struggled for form in Turin, is now on the brink of being eliminated from the season-ending tournament.
The defeat means Alcaraz has to hope for an unlikely straight-sets victory for Russian Andrey Rublev, who has lost his last six Finals matches, over Norwegian Casper Ruud to have any chance of getting through.
Zverev's qualification from the John Newcombe Group means that three of the four semi-final spots have been filled, with Jannik Sinner and Taylor Fritz through from the Ilie Nastase Group.
