Hammel (1-0), obtained in a February trade with Colorado, made his Orioles debut a memorable one, blanking the Twins on no hits until Justin Morneau's lead-off double in the eighth.
The right-hander finished by allowing one run on two hits, walking three and striking out five for Baltimore, which notched its seventh straight win over the Twins.
Jim Johnson collected his second save with a 1-2-3 ninth.
J.J. Hardy socked a first-inning solo homer and Wilson Betemit added a two-run double for the O's.
Anthony Swarzak (0-1) made an emergency start after scheduled Minnesota hurler Liam Hendricks was hospitalized with food poisoning.
Swarzak yielded one run on four hits over five frames.
Josh Willingham had the only RBI for Twins, who opened the season at 0-3 for the first time since 1981.