Doubront, a southpaw vying for Boston's No. 5 job and out of options, danced around eight hits and a walk, lasting 4 2/3 innings. He gave up two runs, walked one and struck out three on 74 pitches, 49 for strikes.
"He looks like what a big league pitcher should look like, so I wouldn't think that it would be out of the question for him to be a starter for our team," manager Bobby Valentine said of Doubront before the game.
Doubront was coming off tossing four shutout innings against the Yankees in his last start.
Marquis' day was done after a leadoff single in the fifth, closing a start that was similar to his last. He gave up three runs in four-plus innings against Boston on Monday, after allowing four runs in as many innings against the Cardinals on Thursday.
Marquis' line Monday included two walks, two strikeouts and five hits on 70 pitches, 43 for strikes.
"I felt like I had good life on my ball, good life and good extension," Marquis said. "The two things that got away from me that I didn't like was the [Jarrod] Saltalamacchia walk and the hit by pitch to [Kevin] Youkilis. Other than that, I felt like I threw the ball where I wanted to and got the results I wanted."
Jamey Carroll, who had been struggling at the plate this spring, had two hits for the Twins, while Ben Revere collected three. Jacoby Ellsbury had a pair of hits for the Sox, including an RBI single in Boston's three-run third inning.
Josh Willingham drove in Minnesota's first two runs, one on a groundout in the first inning, and the next on a single in the third.
Up next: The Twins have an off-day on Tuesday, but return to action on Wednesday with right-hander Liam Hendriks set to start against the Tigers at 12:05 p.m. CT in Lakeland. The game can be seen on MLB.TV. Hendriks has yet to allow a run in seven innings this spring. Left-hander Andy Oliver starts for Detroit.