Willingham gave the Twins an early lead with a leadoff home run, his first of the spring, in the second inning.
Red Sox slugger Mike Napoli tied things up when he opened the bottom half of the frame with a homer to center field.
The Sox added three more runs in the third on Napoli's two-run double, scoring Shane Victorino and Dustin Pedroia, with Xander Bogaerts' double scoring Napoli.
Red Sox right-hander Jake Peavy, making his third start, went five innings, giving up one run on three hits and a walk with three strikeouts. Peavy is on track to start the Red Sox's home opener, Friday against the Brewers.
Trailing, 4-1, the Twins took the lead in the seventh. With lefty Tommy Layne on the mound, Walker, who is ranked the club's No. 14 prospect hit a two-run home run on the first pitch of his first plate appearance in a Grapefruit League game. Pinto gave Minnesota a lead later in the inning with a three-run shot off Layne.
The Twins and Red Sox, Lee County rivals, split their Grapefruit League season series, 3-3.
Up next: Right-hander Ricky Nolasco is scheduled to start on Opening Day for the Twins in Chicago against the White Sox at 3:10 p.m. CT on Monday. Nolasco went a combined 13-11 with 3.70 ERA for the Marlins and Dodgers last season, before joining the Twins as a free agent in December.
In eight Major League seasons he is 89-75 with a 4.37 ERA. In five Grapefruit League outings, Nolasco went 0-2 with a 5.50 ERA. He was the Opening Day starter last season for the Marlins at Washington. Nolasco will be opposed by White Sox left-hander Chris Sale.
The Twins will be opening the regular season during the month of March for just the third time in team history, along with March 31, 2003, when they beat the Tigers, 3-1, in Detroit, and March 31, 2008, a 3-2 win over the Angels at the Metrodome.