The trouble started early for Gee, who loaded the bases on two walks and a hit batsman in the first. Gee then walked Alex Avila to force in a run, and plunked Avisail Garcia to plate another.
Another walk and two wild pitches put a pair of runners in scoring position for the Tigers in the second inning, allowing Cabrera to come through with his two-run single. Two batters later, Tuiasosopo launched his first spring home run over the left-field wall.
"I don't know what happened," Gee said. "I literally just could not throw the baseball anywhere I wanted it to go. It happens, but we'll keep working and figure it out."
Cabrera finished 2-for-4 with two singles, two RBIs and two runs scored. He and first baseman Prince Fielder were both scheduled to make the 2 1/2-hour trip from Lakeland, Fla., but a flat tire forced Fielder to turn around on Florida's Turnpike.
"That was a pretty good replacement today," Tigers manager Jim Leyland said of Tuiasosopo, who subbed for Fielder at first base and also had an RBI double. "I don't think it'll be the Lou Gehrig story, but. ... That [homer] was a bomb against the wind. That was the loudest ball of the spring."
The Mets fought back off Tigers starter Doug Fister in the bottom of the second inning, rallying for their first run on a Mike Baxter walk and consecutive singles by Zach Lutz and Anthony Recker. But Fister escaped that jam with a strikeout and a double play, then mowed down the side in order in the third and struck out the final three batters he faced in the fourth. Fister exited after that, having limited the Mets to one run on three hits and two walks.
Tigers closer candidate Bruce Rondon tossed a 1-2-3 ninth inning with a strikeout.
Up next for the Tigers: Right-hander Rick Porcello (2-1, 2.08 ERA) will make his fifth start of the spring for the Tigers, who face the Blue Jays on Friday in a 1:05 p.m. ET contest at Joker Marchant Stadium in Lakeland, Fla., live on Gameday Audio. The 24-year-old has given up three runs over 13 innings with 14 strikeouts and no walks. Toronto will counter with left-hander Ricky Romero (0-0, 6.35 ERA).
Anthony DiComo is a reporter for MLB.com. Follow him on Twitter @AnthonyDicomo. This story was not subject to the approval of Major League Baseball or its clubs.