Hicks' key hit driving in Trevor Plouffe was backed by four shutout innings by the Twins' bullpen. Anthony Swarzak (1-0) earned the win with 1 1/3 innings of scoreless ball, while Brian Duensing, Jared Burton and Glen Perkins (2nd save) completed the sterling mop-up job.
Justin Morneau supplied a two-run double for the Twins, who took the rubber match of a three-game set to win their second consecutive series starting the season.
Minnesota starter Pedro Hernandez, making just his second career appearance, allowed three runs on four hits and three walks over five innings.
Jason Hammel (1-1) absorbed the loss for Baltimore, yielding four runs on four hits over 6 2/3 innings.
J.J. Hardy homered for the Orioles.