Gaby Sanchez was the first to go deep for Pittsburgh with a solo shot in the second off Twins starter Liam Hendriks. Tony Sanchez added a solo homer of his own in the third before McCutchen crushed a two-run blast off the scoreboard in left.
The three homers were the only three hits given up by Hendriks, who gave up four runs in three innings.
"Everything was feeling good, but I just couldn't repeat myself today," Hendriks said. "I almost felt too loose and I was a little bit all over the place. I just couldn't throw back-to-back pitches where I wanted to. It was a tough day. I was able to get through most of it, but I ran into some trouble in the third because I was getting behind."
Left-hander Jonathan Sanchez tossed two innings for the Pirates. He gave up a solo blast to Josh Willingham -- his second homer of the spring -- in the first before surrendering another run in the second on an RBI single from Brian Dozier.
The Twins tied the game with two runs in the fifth against Pittsburgh reliever Stolmy Pimentel. Aaron Hicks drove home his 13th run with an RBI single before later scoring on a passed ball with Ryan Doumit at the plate.
Up next: Lefty Jeff Locke makes his team-high fourth start when the Pirates and Orioles hook up again, this time at McKechnie Field in Bradenton, on Monday at 1:05 p.m. ET on Gameday Audio. But of greater interest will be what follows the spring's fourth game between the teams, as manager Clint Hurdle will meet with his staff to discuss the first cuts from among the 62 players in the Bucs' big league camp.
Rhett Bollinger is a reporter for MLB.com. Read his blog, Bollinger Beat, and follow him on Twitter @RhettBollinger. This story was not subject to the approval of Major League Baseball or its clubs.