The Red Sox had brought in outfielder Darnell McDonald (0-1) to pitch in the top of the 17th and J.J. Hardy collected his fifth hit of the game, a two-out double.
Nick Markakis walked and Jones followed by smacking a pitch into the seats above Fenway Park's "Green Monster" left field wall, breaking a 6-6 tie.
Orioles first baseman Chris Davis (1-0) earned the victory by tossing two shutout frames, striking out Adrian Gonzalez and inducing McDonald to ground into a game-ending double play in the bottom of the 17th.
Hardy launched two solo homers for Baltimore, which completed a three-game sweep of the Red Sox and grabbed sole possession of first place in the American League East with a 19-9 record.
Will Middlebrooks cracked his first major-league homer -- a grand slam -- and Ryan Sweeney went 4-for-8 with an RBI for Boston, which dropped a fifth straight game.
S. Carolina GOP Governor Nikki Haley breaks wood with hands [VIDEO]
Christian anarchists take credit for stealing racy calendars from Mall