The win lifts the Orioles to a 4-0 start in 2016.
Tillman (1-0) gave up a run on four hits in five innings of work, striking out five and walking two. T.J. McFarland and Brad Brach held the Rays to two baserunners in four innings of relief.
The O’s touched up Chris Archer (0-2) for six runs on 10 hits in five innings of work. Chris Davis, Jonathan Schoop, Nolan Reimold and Manny Machado each hit solo homers for Baltimore.