All four Minnesota runs in the sixth were unearned courtesy of a throwing error by pitcher John Lackey.
The Twins won the final three games of the four-game series, a streak that came after they had lost five out of seven. Boston has dropped six of its last seven contests.
Boston held a 2-1 lead heading into the sixth, but Joe Mauer opened the inning with a single off Lackey (1-3).
Josh Willingham flew out to center and Justin Morneau drew a walk. Trevor Plouffe then hit a grounder back to Lackey, but his throw to second was wild. Mauer scored on the error and Morneau went to third, from where he came in on a sacrifice fly by Ryan Doumit.
Arcia followed with his homer to right that gave the Twins a 5-2 lead.