Arias collected two hits and Kole Calhoun had an RBI sacrifice fly in the third inning to send the Guardians (65-70) to their third win in a row and fifth in their last seven games.
Randy Arozarena and Rene Pinto each had an RBI double for the Rays (82-53), who saw their four-game winning streak come to a halt.
Tampa Bay was nursing a slim 2-1 lead before Cleveland ignited its offense in the seventh inning.
Andres Gimenez singled off Tyler Glasnow (7-5) to begin the seventh and advanced to third on a stolen base and a lineout. Arias' single to left field plated Gimenez to forge a tie before Naylor's RBI double gave the Guardians a 3-2 lead.
The late uprising made a winner out of Eli Morgan (5-2), who allowed two hits in one scoreless inning of relief of starter Cal Quantrill. Trevor Stephan struck out two batters in a scoreless eighth inning to bridge the gap to Emmanuel Clase, who retired the side in the ninth to secure his 37th save of the season.
Tampa Bay got off to a fast start by scoring one run in each of the first two innings.
Brandon Lowe worked a one-out walk off Quantrill in the first inning and came around to score on Arozarena's double off the top of the left-field wall. The double extended Arozarena's hitting streak to five games.
The Rays doubled the advantage in the second after Jonathan Aranda worked a two-out walk and scored on Pinto's double to left field.
Cleveland halved its deficit in the third inning. Myles Straw doubled to lead off the inning against Glasnow, advanced to third on an infield single and scored on Calhoun's sacrifice fly to left.
—Field Level Media