Ramos is in competition with Jake Odorizzi, who pitched the game's last four innings Thursday, and Erik Bedard, who was scheduled to start Friday.
Ramos removed himself from a fourth-inning jam when he caught Trevor Plouffe looking at a slider for the third out, stranding runners at the corners.
"I got ahead, threw strikes, kind of pitched to contact, and things worked out," Ramos said. "The defense made some big plays, and that definitely helped my cause."
Evan Longoria bare-handed Brian Dozier's chopper to third and threw him out at first for the first out of the game. Desmond Jennings made a diving catch for the second out of the second when Plouffe hit a sinking line drive to center field. Rays shortstop Yunel Escobar then worked his magic in the third, going to his left to steal a base hit from Pedro Florimon before flipping to Ben Zobrist, who stepped on second and threw a strike to first to complete the double play.
Grant Balfour struck out Dozier swinging to end the fifth, giving the Rays' closer his first back-to-back appearances of the spring.
Odorizzi followed, allowing four runs (three earned), six hits, and a walk in four innings. He also struck out three.
Meanwhile, the Twins entered the evening still looking to decide who would be their fifth starter. Scott Diamond, Samuel Deduno and Kyle Gibson are the remaining contenders, and Diamond stated his case Thursday night.
The left-hander pitched four scoreless frames before leaving the game after walking the bases full with one out in the fifth. Brian Duensing took over, and Zobrist grounded to first to drive home Ryan Hanigan. Longoria added a two-run double to put the Rays up, 3-0, with all three runs charged to Diamond. The teams traded runs late, with Tampa Bay adding two runs in the seventh before Minnesota made its run against Odorizzi, which included a two-run single by Florimon.
Up next: Right-hander Ricky Nolasco will face the Mets on Friday in a 12:05 p.m. CT start at Hammond Stadium on MLB.TV. Nolasco, who was named the club's Opening Day starter last week, has a 3.27 ERA in three outings this spring. Right-hander Dillon Gee starts for the Mets.