Britton lasted only five innings and allowed five runs and eight hits, with three walks, no strikeouts and two home runs. He threw 91 pitches, 55 for strikes.
Kevin Gausman replaced Britton, who had permitted three earned runs in his last two starts covering 12 1/3 innings.
The Orioles could option Britton to Triple-A Norfolk while activating left-hander Wei-Yin Chen, who will start Wednesday night.
Britton walked No. 9 hitter Leonys Martin with one out in the sixth, but the Rangers center fielder was tagged out at second base after Britton caught him breaking early at first. Ian Kinsler singled, Jurickson Profar walked and Nelson Cruz tied the game with a single into left field.
Adrian Beltre followed with his second home run, a three-run shot, and Britton's night was coming to an end.
The Orioles scored twice in the bottom of the fifth on J.J. Hardy's two-out, two-run single to reduce the Rangers' lead to 5-4. Both runs were unearned.
Errors by Beltre and first baseman Robinson Chirinos put runners on the corners with no outs, but the Orioles almost squandered the opportunity. Rangers starter Martin Perez retired Manny Machado and struck out Adam Jones, who swung at a ball that bounced in the dirt earlier in the at-bat. Perez hit Chris Davis to load the bases, and Hardy singled into left field.
Gausman hasn't allowed a run in eight relief innings. The Orioles helped him out in the top of the sixth by turning their third double play after Elvis Andrus reached on an infield hit.
Tonight's attendance: 29,160
Update: Gausman allowed his first runs in relief after eight scoreless innings when the Rangers scored twice in the seventh to increase their lead to 7-4.
Another walk to Martin started the trouble. Why, oh why, do the Orioles have such trouble with guys at the bottom of the lineup?
Profar had an RBI single off Gausman, and Brian Matusz let an inherited runner score on A.J. Pierzynski's single.
Matusz had stranded 25 of 27 inherited runners this season 39 of 41 over two seasons.
Update II: Beltre finished with five RBIs tonight and the Orioles lost to the Rangers 8-4 at Camden Yards.
Beltre's two-out, broken-bat single into center field in the ninth inning off Darren O'Day completed the scoring, and the Orioles (49-42) lost for the sixth time in their last eight games.
Beltre reached base in all five trips to the plate, with two homers, two singles and an intentional walk. The Orioles should have gone with five intentional walks.