Britton (4-1) surrendered five hits while walking two and striking out two for the O's, who took the first of a three-game series against the Red Sox.
Adam Jones drove in two runs with a pair of sacrifice flies while Mark Reynolds and Matt Wieters added an RBI apiece for Baltimore.
The Red Sox had a five-game winning streak snapped.
Clay Buchholz (1-3) was saddled with the loss. He was tagged for 12 hits in 6 2/3 innings, surrendering four runs while walking two and fanning five.
Kevin Youkilis drove in Boston's only run with a sac fly.