Park's homer made it a one-run game, and the Twins took the lead in the fifth, keyed by doubles from Joe Mauer and Miguel Sano. Max Kepler, ranked as the No. 44 prospect by MLBPipleline.com, followed Sano's RBI double with an RBI single to give the Twins the lead.
Right-hander Kyle Gibson started for the Twins, reached his 45-pitch limit after two innings. He gave up two runs on four hits and three walks.
"I just didn't have the fastball command today," Gibson said. "The sinker wasn't really sinking. The glove-side sinkers weren't very good. I was throwing it where I intended it to throw it, but it just wasn't sinking and was like a four-seamer basically."
The Marlins scored early on an RBI single from J.T. Realmuto in the first before tacking on a run in the second on a sacrifice fly from Marcell Ozuna. They took the lead in the seventh on a pair of RBI groundouts from Dan Black and Tomas Telis.
Right-hander Jarred Cosart made his first start of the spring for Miami, tossing two scoreless innings. He gave up one hit and walked one with a strikeout.
"Just knocking the rust off," Cosart said. "Nothing compares to a real game. Obviously, it's Spring Training still. You can't simulate in the sim games and practices and bullpens, so I had a lot more adrenaline than I thought I would for a Spring Training game."
Sano went 2-for-2. Twins catcher Juan Centeno added an RBI single in the seventh to tie the game.
The Marlins took the lead in the eighth on an RBI single from Yefri Perez off pitching prospect Randy Rosario.
Up next for the Marlins: Non-roster invitee Chris Narveson starts against the Red Sox at 1:05 p.m. ET on Saturday in Fort Myers. The game can be watched live on MLB.TV. The lefty has given up three runs over three innings spanning two spring outings.
Up next for the Twins: He'll be piggybacked by right-hander Trevor May, who is competing for the final spot in the rotation, starts things off when the Twins travel to face the Orioles at 12:05 p.m. CT in Sarasota. Listen on Gameday Audio.
Rhett Bollinger is a reporter for MLB.com. Read his blog, Bollinger Beat, follow him on Twitter @RhettBollinger and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.