Britton (1-0), called up after Orioles hurler Brian Matusz was placed on the 15-day disabled list, responded with an impressive effort, holding the Rays to one run on three hits with six strikeouts over six innings.
Mark Reynolds paced Baltimore's offense with two doubles and two runs batted in as the Orioles swept the Rays at Tropicana Field for the first time since 2005.
Wade Davis (0-1) took the loss for Tampa Bay, yielding four runs on eight hits over 6 1/3 innings.
Tampa Bay announced before the game that third baseman Evan Longoria had been placed on the 15-day disabled list with a strained oblique.
2014: The Year in Music [PHOTOS]