Tampa Bay opened the scoring on Miller's two-run single off Baltimore's Dale Thayer in the top of the third, and Casali drove in former Oriole Steve Pearce in the fourth.
After Chris Davis' RBI groundout scored Manny Machado to make it 3-1 in the bottom of the fourth, Kiermaier's RBI triple off Todd Redmond helped the Rays pull away with a six-run fifth.
Redmond was charged with four runs, while O's Minor League pitcher Jon Keller allowed three and didn't record an out.
Machado and Adam Jones picked up RBIs during a four-run fifth for the Orioles.