The Twins got on the board first with two runs in the third against Orioles right-hander Kevin Gausman, who was Baltimore's first-round choice in last year's First-Year Player Draft.
Aaron Hicks, who went 3-for-5 with two RBIs and two runs, started the inning off with an RBI triple to score Parmelee before Brian Dozier brought Hicks home with a single to left.
The Orioles tied it with two runs in the fourth thanks to an error by shortstop Pedro Florimon. The runs came off reliever Alex Burnett, who replaced Twins starter Liam Hendriks after he left the game with a bruised right hand. The right-hander suffered the injury on a line drive from Brian Roberts after pitching 2 2/3 scoreless innings. He is considered day to day.
"It was just precautionary," said Hendriks, who was slated to throw 85-90 pitches. "I feel fine. The ball was coming out good. It was just one of those things where they took me out just in case it was something more serious. But the pitch count thing does stink a little bit."
Ramirez gave the Twins a 3-2 lead with an RBI double in the fourth, but Matt Wieters tied it with a solo shot in the fifth off reliever Casey Fien.
The Twins broke it open with a four-run fourth that started with Willingham's solo blast. Miguel Sano had an RBI single, Parmelee added an RBI double and Ramirez brought home a run on an RBI groundout.
Ryan Doumit's sacrifice fly made it 8-4 in the sixth and Hicks had an RBI single in the seventh to make it 9-4.
Jared Burton and Glen Perkins each pitched scoreless innings in relief.
Up next: Right-hander Vance Worley is scheduled to start for the Twins in a 12:05 p.m. CT game on Wednesday against the Pirates in Bradenton. Worley is likely to be Minnesota's Opening Day starter, as he's starting five days before the regular season begins against the Tigers at Target Field. However, the Twins have yet to officially name an Opening Day starter. Right-hander A.J. Burnett is scheduled to take the mound for Pittsburgh. The game can be heard live on Gameday Audio.
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.