Los Angeles scored four times in the ninth inning to capture its 18th victory in 21 games.
Tampa Bay held a 6-1 lead heading into the eighth and even though the Dodgers produced two runs in that inning, it appeared the Rays had things under control.
Rodney (4-3) came on in the ninth inning in search of his 28th save, but he was able to retire only one of the seven men he faced.
Nick Punto then doubled home Ellis to bring the Dodgers within one and another double from Gonzalez tied the contest at 6-6.
Yasiel Puig, who had driven in one of the Los Angeles runs in the eighth, was walked intentionally and that brought up Jerry Hairston.
Hairston hit a hot grounder back to Rodney on the mound, setting up what could have been a double play that would have brought about extra innings. Instead, Rodney's throw to second base sailed into center field and Gonzalez easily scored the winning run.
The comeback gave the win to Ronald Belisario (5-6), the fifth Los Angeles pitcher who retired the side in order in the top of the ninth.
Tampa Bay missed a chance to move within a game of Boston at the top of the National League East.