Danny Santana's triple to right field off Orioles prospect Mike Wright tied it up at 2 in the top of the eighth.
First baseman Chris Davis, who led the Majors with 53 home runs last season, hit a solo homer to center field off righty Trevor May with one out into the sixth inning to give the Orioles a one-run edge.
Minnesota broke a scoreless tie in the fourth when Ramirez's two-out single scored Chris Colabello from second base.
Top Orioles prospect Kevin Gausman got out of the inning with no further damage as Jason Kubel was tagged out trying to advance to third on the play. Gausman retired the first five batters he faced in the 24-pitch, two-inning outing.
The O's tied it up in the bottom half of the frame, as Nick Markakis, who had two hits in his first two at-bats, scored on Aaron Thompson's error.
Baltimore starter Bud Norris pitched two scoreless innings in his first spring start, striking out two and allowing a hit and a walk. Norris, considered the leading candidate for the team's fifth-rotation spot, was pleased with how his first Grapefruit League game with Baltimore went.
"It went really well," Norris said. "It's more about getting out there, getting back into competition and just feeling comfortable. I've been through a couple now, so this is a new one to me here in Sarasota, but just to get out there and play baseball again is what you like to do. I had good results. I felt really good, and that's obviously the goal -- is to leave here healthy."
Twins starter Vance Worley, who is trying to make the club as a fifth starter along with Samuel Deduno and Scott Diamond, cruised through three scoreless innings. Worley, who is out of Minor League options, allowed just a single to Markakis.
"Today, I was able to locate my fastball, get ahead in the count," Worley said. "I had some opportunities for offspeed pitches to keep those guys off-balance."
Up next: Wei-Yin Chen will make his Grapefruit League debut against the New York Yankees on Tuesday night in Tampa, Fla. Chen will be opposed by right-hander David Phelps in the 7:05 p.m. ET game, which will air on MLB.TV.