Dillon and relievers Dana Eveland and Gonzalez Germen shut out the Twins through seven innings, before Minnesota tied the game with three runs off Vic Black in the eighth. Eveland, who signed a Minor League contract in February and will likely start the season at Triple-A Las Vegas, struck out three and walked one in 2 1/3 hitless innings. Germen gave up only one hit during his scoreless 1 2/3-innings stint.
Chris Young connected for his first home run of the spring, a drive over the left-field wall, to give the Mets a 1-0 lead in the first inning.
The Mets added another run in the third when Matt Reynolds led off the bottom half of the inning with a single, hustled to third on a single by Matt den Dekker and scored on a sacrifice fly by Daniel Murphy.
Both runs were charged to Twins starter Scott Diamond, who went 3 2/3 innings. Diamond registered six strikeouts and allowed only three hits, but issued three walks.
Outfielder den Dekker started another Mets rally in the fifth when he singled, went to third on a single by Young and scored on a single by Josh Satin to give New York a 3-0 lead.
In the eighth inning, Black allowed three hits and issued two walks as the Twins knotted the score on Eduardo Escobar's two-run single and an RBI single by Jermaine Mitchell.
"We gave up some early like yesterday and we held on from there, and we missed some opportunities," Twins manager Ron Gardenhire said. "We're still missing some opportunities early in the game to get a runner in, get him over and all those things. We've got to get better there."
Up next: Ricky Nolasco makes his first start since officially being named the Opening Day starter against his former team, the Marlins, at 12:05 p.m. CT on Sunday at Hammond Stadium. Over two spring outings, he has given up two runs on six hits in six innings. One of his starts was rained out. Watch the game live on MLB.TV
Steve Dorsey is a contributor to MLB.com This story was not subject to the approval of Major League Baseball or its clubs.