Tillman (5-1), who won his fourth straight start, held the Mariners without a hit until Mike Carp broke up the no-hitter bid with a one-out single in the fifth.
The right-hander ended up yielding one run on five hits over 7 1/3 innings, walking one and striking out five as Baltimore took the opener of a three-game series.
Pedro Strop got the final two outs of the eighth and Jim Johnson racked up his 33rd save in Baltimore's third straight win.
The O's scored all three of their runs in the third when Mark Reynolds delivered an RBI double and Markakis followed with a two-run shot.
Seattle's Jason Vargas (12-8) absorbed the complete-game loss, yielding three runs on eight hits over eight frames. He walked one and struck out two.
Celebrity Families of 2014 [PHOTOS]