Starting and winning pitcher Rich Hill (3-1) drove in a run with a single and went 6 2/3 innings while allowing five hits and two runs.
Philadelphia lost its fourth straight, all at home. The defending World Champion Phillies have a 23-9 record on the road this season, but are only 13-20 at home.
Wieters had a two-run double in the second inning to overcome an early 2-0 deficit and then scored the go-ahead run on a single by Hill.
Reimold's homer came in the ninth to give Baltimore a 5-2 lead and Markakis added insurance in the inning with a two-run double.
Antonio Bastardo (2-2) allowed five hits and four runs over seven innings to take the loss.
Copyright 2009 by United Press International.