Glenn Perkins picked up the win for the Twins, he pitched a scoreless ninth inning. Boston reliever Andrew Miller was tagged with the loss after giving up Parmelee's blast.
Parmelee's homer was his third hit of the night. He finished 3 for 4. Kurt Suzuki also had three hits for the Twins.
David Ortiz had a big night for the Red Sox. He homered twice and was 4 for 5 with 4 RBIs.
But it wouldn't stay that way as the Red Sox rallied to score one in the sixth and three in the seventh to erase the Twins lead and even the score at six.
The normally solid Twins bullpen collapsed in the seventh. Michael Tonkin gave up three runs and three hits in just two-thirds of an inning, and Brian Duensing and Matt Guerrier failed to get an out to get the Twins out of the inning.
Caleb Thielbar got the final out of the inning for the Twins, but not until the damage was done.
Ricky Nolasco pitched well, but did not factor in the decision. He gave up three runs in six innings, and left with the Twins leading 6-3.
The score remained tied at six until Parmelee's home run.
The Twins and Red Sox continue the series on Wednesday.