With Andrew Miller (1-1) on the mound, Kurt Suzuki hit a two-out single to keep the inning alive, and Parmelee followed with a crush over the right field wall for the walk-off win.
Eduardo Nunez hit a two-run home run, Brian Dozier drove in two, while Joe Mauer and Suzuki each had an RBI for the Twins, who have won three of their last four.
Ricky Nolasco gave up three runs on six hits over six innings of work in the start for Minnesota. Glen Perkins (1-0) worked a scoreless ninth for the win.
David Ortiz went 4-for-5 with two home runs and four RBI, Shane Victorino was 3-for-5 with an RBI and two runs scored, and Jonny Gomes brought home a run for the Red Sox, who had won their previous two. Jake Peavy gave up six runs on nine hits in just 4 1/3 innings of work.
Chris Parmelee's home run in the ninth inning gave the Minnesota Twins an 8-6 win over the Boston Red Sox in the opener of a three-game set.