Arcia came to the plate leading off the seventh and belted a 3-2 pitch from Houston starter Brad Peacock into the first row of seats in right field, boosting Minnesota to a three-game series sweep on the heels of a sweep by Kansas City, all at home.
Justin Morneau supplied a two-run homer, his 10th of the season, in the first inning for the Twins.
Caleb Thielbar (2-1) notched the final two outs of the sixth to collect the decision and Glen Perkins secured the victory with his 27th save. Twins starter Mike Pelfrey got through five innings, giving up the two Astros runs in the no-decision.
Peacock (1-4), recalled from Class AAA Oklahoma City before the game, surrendered three runs on four hits through seven innings, striking out 10.