Derek Dietrich's RBI single in the sixth inning provided Miami with an insurance run.
Minnesota's Phil Hughes and Miami's Tom Koehler each gave up a run, but for the most part, they did their jobs.
Byron Buxton, ranked by MLB.com as the No. 1 prospect in the game, went 0-for-5 for Minnesota.
Hughes, in his first Grapefruit League action, worked 2 2/3 innings, and his fastball was between 92-94 mph.
Koehler, in two innings, maxed out at 95 mph. He allowed one run on three hits.
The Twins struck first, scoring on Eduardo Escobar's sacrifice fly to right field in the second inning. Koehler actually did a good job minimizing the damage, because Minnesota loaded the bases with no outs.
The Twins left 11 men on base, going 0-for-9 with runners in scoring position.
"Situational hitting wasn't very good at all," manager Ron Gardenhire said. "A couple of situations where we had a chance to drive in a run and we swing first pitch at a bad pitch and pop it up."
Koehler also didn't get much luck, because Aaron Hicks' single to left dropped between left fielder Christian Yelich and shortstop Adeiny Hechavarria. Both had a chance to make the play. The Marlins committed five errors on the afternoon, including one each by Hechavarria and Saltalamacchia.
Chris Colabello led the inning off with a single, and he scored on Escobar's fly ball to right field. Koehler regrouped, struck out Eric Fryer and retired Doug Bernier on a line drive to left.
Miami responded off Hughes with back-to-back, two-out singles. Saltalamacchia walked to open the inning. With two outs, Greg Dobbs singled and Ed Lucas slapped an RBI single to right.
Up next: The Twins will return to Fort Myers, Fla., on Wednesday to host the Orioles in a 6:05 p.m. CT game on MLB.TV. Right-hander Mike Pelfrey will make his second Grapefruit League start after throwing two scoreless innings against the Red Sox last Friday. Lefties Scott Diamond and Glen Perkins and righty Jared Burton are among those also scheduled to pitch. Diamond is battling for the fifth spot in the Twins' rotation, and he made one previous start this spring, giving up one run in two innings.