Wei-Yin Chen (4-3) came off the disabled list to cool off the Rangers, who had scored at least five runs in each of their last six games.
Manny Machado opened the scoring with an RBI triple in the third and then came in on a wild pitch thrown by Josh Lindblom (1-3).
Baltimore broke things open in the fourth when Brian Roberts singled in a run and then scored along with J.J. Hardy on Reimold's fifth homer of the year.
Adrian Beltre had one of only three hits allowed by Chen in seven innings and a fielder's choice grounder by Beltre in the sixth drove in the lone Texas run.
In his previous six games Beltre had batted .636 with 14 hits, six home runs and 10 RBI.
Lindblom gave up all six runs on nine hits in 5 1/3 innings.