Jones' shot in the fifth inning put the Orioles ahead 5-0 after J.J Hardy had clouted a two-run homer in previous frame.
Britton (1-1), making the start after being recalled from Class AAA Norfolk, handled the Tigers on one run over 5 1/3 innings, allowing five and three walks while striking out one.
Jim Johnson closed out the triumph with his major league-best 26th save as the O's evened their three-game set.
Detroit's Justin Verlander (8-5) saw his five-start unbeaten streak broken, surrendering five runs on seven hits over five full innings.
Matt Tuiasosopo cracked a solo homer for the American League Central-leading Tigers.