Hall of Famers Carl Yastrzemski and Jim Rice were joined by Luis Tiant and Dwight Evans in a pregame ceremony.
Josh Beckett got the start for the Red Sox, holding the Twins to one hit and no runs over two innings. Beckett walked two and struck out none, throwing 36 pitches.
"I think it's just nice to get back out there and get the adrenaline going," said Beckett. "That's definitely different than anything we've had so far, even with live BPs. I think right now it's just building up. I felt like I stayed strong through it."
Francisco Liriano, Minnesota's ace lefty, gave up a hit and a walk in his two innings, striking out two.
"The first batter, I was kind of all over the place, but after that, I kind of made some adjustments," said Liriano, who threw 13 of his 25 pitches for strikes. "I was throwing the ball down and working the fastball better."
Mike Aviles, trying to become Boston's starting shortstop, put his team ahead with a two-run single up the middle in the bottom of the fourth that broke a scoreless tie.
Ben Revere, expected to be the Twins' starting left fielder, chipped in with two hits and two RBIs. His second hit tied the game in the top of the seventh.
Andrew Miller, one of several pitchers vying for Boston's fifth rotation spot, was impressive, striking out three over two innings.
Jason Bulger, competing for a spot in Minnesota's bullpen, gave up Anderson's grand slam and five runs overall in just one-third of an inning.
Up next for the Twins: The Twins play their first and only night game of the spring on Monday, as they host the Red Sox at Hammond Stadium at 7:05 p.m. ET. Right-hander Jason Marquis is set to make his Grapefruit League debut for Minnesota. Joe Mauer, Justin Morneau, Denard Span and Josh Willingham -- who didn't play on Sunday -- are expected to return to action Monday night.
Up next for the Red Sox: The Red Sox take the short bus ride to Hammond Stadium to play the Twins for the second time in two days. The game will be played under the lights at 7:05 p.m. Clay Buchholz will make his first start since June 16 of last season, when he injured his back. Vicente Padilla, competing for a rotation spot, will come out of the bullpen.