Hardy, who was let go by Minnesota as a free agent after last season, connected for a solo blast in the fifth inning to put Baltimore ahead 2-1.
Matt Wieters added a solo shot in the sixth for the Orioles, who took the opener of a four-game series.
Britton (7-9), who came off the disabled list before the game, yielded one run on six hits and overcame four walks to end a personal five-decision losing streak.
The left-hander, who landed on the DL Aug. 5 with a left shoulder strain, logged his first win since June 8, a stretch of eighth starts. Kevin Gregg tossed a perfect ninth for his 18th save.
Minnesota's Carl Pavano (6-10) yielded four runs on nine hits over seven innings.