The second-seeded Gators (53-17) will play South Carolina or Virginia in the best-of-three championship round starting Monday.
Alex Panteliodis limited Vanderbilt (54-12) to three hits in six innings before five relievers squandered all of his 4-1 lead.
Daniel Pigott singled and Cody Dent and Nolan Fontana reached on back-to-back bunts before Tucker drove a ball into deep left. The Gators were up two runs after Mark Lamm's breaking ball in the dirt bounced away from Curt Casali, allowing Dent to come home.
Austin Maddox (3-0) earned the win. Oakland Athletics first-round draft pick Sonny Gray (12-4) took the loss for Vanderbilt, which was in the CWS for the first time.