Austin Pruitt took over from Snell to start the sixth, and the Marlins greeted him with seven consecutive hits, including a two-run single by J.T. Realmuto and a two-run double by Giancarlo Stanton.
More troubles followed for the Rays in the seventh, when rookie Jose Alvarado made his Major League debut. Realmuto, who had four RBIs in the game, tripled home two to highlight the three-run inning.
Prior to the bullpen meltdown, the Rays held a 4-2 lead thanks to Kevin Kiermaier's two-run single and a solo homer by rookie Daniel Robertson projected at 425 feet to center field.