Shane Victorino, appearing in just his second game of the spring due to nagging injuries, drove in the other unearned run that inning with a line single to center.
Victorino also had a bunt single and scored the go-ahead run in the fifth, when shortstop Danny Santana's fielding error led to a two-out rally.
The Twins made four errors overall, leading to four unearned runs.
Red Sox: Right-hander Jake Peavy, making his first appearance of the spring training after cutting his finger preparing for a fishing trip March 1, worked three-plus innings and allowed one run on two hits and two walks. Peavy's fastball hit 93 mph several times on the Hammond Stadium scoreboard radar.
"It was nice to get out there for the first time in a game-like atmosphere and to be able to use all your pitches and be able to use that next step," Peavy said. "It was nice to ramp up the intensity a little bit more than I had been."
Twins: Hughes gave up four hits (all singles) and walked none in shaving his spring ERA to 1.04. He was unable to work around two errors in the third, however, and Twins pitching coach Rick Anderson said Hughes admittedly "let it get away from him mentally a little bit."
Hughes didn't mind laboring near the end of his 65-pitch outing.
"I thought overall it was pretty good," he said. "It's good to get those innings where you have to throw a bunch of pitches and get through it and get that arm strength going."
Red Sox: Outfielder Grady Sizemore, who missed the past two seasons with back and knee injuries, played five innings in a Class A game and went 1 for 2 with a walk.
Twins: Shortstop Pedro Florimon, coming off Feb. 17 appendectomy, took batting practice and is slated to play three innings in a minor league game on Friday. He could make his 2014 Grapefruit League debut as soon as Sunday. ... Right-handed power prospect Miguel Sano won't return to Twins camp until Saturday after undergoing Tommy John surgery on his right elbow on Wednesday in New York City. Sano felt dizzy after taking pain medication and will remain in the hospital through Friday night.
Pitching prospect Anthony Ranaudo topped the list of 12 Red Sox players in the first round of cuts Thursday morning. Ranaudo, a right-handed starter, was optioned to Triple-A Pawtucket along with outfielder Bryce Brentz, third baseman Garin Cecchini, outfielder-first baseman Alex Hassan and right-hander Alex Wilson.
Seven others were reassigned to minor league camp: right-handers Matt Barnes, Miguel Celestino and Noe Ramirez; left-hander Henry Owens; infielder Heiker Meneses, first baseman Travis Shaw and catcher Blake Swihart.