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: The Twins play their second night game of Spring Training on Monday at 6:05 p.m. CT on Gameday Audio, facing the Rays at Charlotte Sports Park. Right-hander Vance Worley, who was acquired in the Ben Revere trade, is set to start for the Twins. Right-hander Roberto Hernandez is scheduled to take the mound for Tampa Bay.
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.