Tillman (13-3) has lost just once in his last 13 starts. He gave up three hits and walked three while throwing 123 pitches. Jim Johnson completed the shutout in a non-save situation.
Adam Jones ignited the Baltimore offense by hitting two of Baltimore's four home runs, a two-run shot in the first and a solo blast in the fifth. He has 22 for the season.
Manny Machado and J.J. Hardy added solo homers in the seventh and eighth innings.
Five of the runs were charged to John Lackey (7-8), who allowed nine hits in 6 1/3 innings.
Pregnant Mila Kunis wins 'Best Villain' at MTV Movie Awards
'Happy' fan videos make Pharrell cry [VIDEO]