Morneau, who entered the game hitting just .108, crushed a two-run blast off Rays right-hander Jeremy Hellickson in the first inning before connecting on a three-run homer off Hellickson in the fourth. It marked Morneau's first two homers of the spring. He finished the day going 2-for-2 with two homers, five RBIs, three runs scored and a walk.
"It feels good," Morneau said of his two-homer effort. "It'd be nice to have it on Opening Day. It's one of those things where you don't necessarily need to hit home runs to know where you're at."
Catcher J.R. Towles also homered for the Twins with a solo shot in the second inning. Joe Mauer, making his third start of the spring at first base, went 2-for-4 with two runs to raise his average to .333.
Jamey Carroll picked up three hits and an RBI, Denard Span provided a two-run triple and Luke Hughes went 3-for-3 with two RBIs for the Twins.
The Twins muscled up again in the sixth inning, as Chris Parmelee and Hughes each added solo homers.
Hughes doubled in two more runs in the eighth inning to finish his day 5-for-5 with a homer, two doubles and five RBIs.
Chris Gimenez homered in the seventh for the Rays, a solo shot.
Hellickson struggled on the afternoon, allowing 10 runs on 11 hits over three-plus innings. He walked two, struck out one and served up three homers.
However, Rays manager Joe Maddon was not discouraged by Hellickson's outing.
"He had good stuff today, I mean that sincerely," Maddon insisted. "I thought he had good stuff. It was his execution that was not so good."
Right-hander Jeff Gray started for the Twins, as Jason Marquis missed his scheduled start because he was tending to a family issue back home in New York. Gray surrendered two runs on two hits, a walk and a hit batter over two innings.
Matt Mangini and Will Rhymes each had an RBI for Tampa Bay in the second inning.
Up next for the Twins: The Twins travel across the state to take on the Cardinals in Jupiter at 1:05 p.m. ET on Sunday, with right-hander Nick Blackburn slated to make the start. Blackburn has been impressive this spring, as he's yet to allow a run over seven innings in Grapefruit League play. Brian Duensing, Kyle Waldrop and Jared Burton are also scheduled to pitch for the Twins. Former Twins right-hander Kyle Lohse will start for St. Louis.