Diamond (2-2) allowed just four hits and two runs in six innings. He took a no-hitter into the fifth inning and lost his shutout when the Tigers bunched together three hits for two sixth-inning runs.
The Twins, however, were up 3-0 before that, with Morneau doubling in Josh Willingham and then scoring when Parmelee singled in the first. Jamey Carroll made the score 3-0 with a run-scoring double in the second.
Detroit starter Anibal Sanchez (3-2) allowed only one other hit in the next four innings but still got the loss.
Minnesota reached the Detroit bullpen for late runs. Pedro Florimon and Morneau drove in runs in the seventh and Parmelee led off the eighth with his second home run of the season.