New York had a five-game winning streak snapped, becoming a victim of four Tampa Bay home runs.
Lobaton gave the Rays a 3-1 lead with his shot to right, Evan Longoria and Matt Joyce hit solo homers in the third and Ben Zobrist added a solo shot in the fifth. Lobaton drove in a fourth run with a fourth-inning single.
Chris Archer (7-5) benefited from the assault to get the win, giving up two runs on just four hits in seven innings.
Hiroki Kuroda (11-9) surrendered all four Tampa Bay home runs in six innings of work to take the loss.
After retiring the Rays in order in the first, Kuroda gave up a leadoff single to Matt Joyce in the second. Kelly Johnson had a base hit one out later and Lobaton came up with two away. He homered on Kuroda's first pitch.