Schoop was joined by teammate Pedro Alvarez, who homered in the third inning off Rays starter Chris Archer as the O's maintained a two-game lead in the American League East.
The Rays, who have a seven-game losing streak, have now lost 23 of their last 26 games. Archer went 7 1/3 innings, dueling Orioles starter Yovani Gallardo, who went only five innings. Rays catcher Luke Maile had two hits and drove in a run in his season debut.
Orioles All-Star closer Zach Britton stranded runners on the corners and picked up his 28th save.