Reliever Clayton Mortensen (0-1) retired the first two men in the Baltimore seventh, but then gave up a single to Manny Machado and walked Nick Markakis.
That brought up Jones, who drove the first pitch from reliever Koji Uehara to left for the game-winning hit.
Chris Davis hit his sixth homer of the year for the Orioles in the second and Jones singled in a run in the sixth. Baltimore took two of three from the Red Sox.
Baltimore had lost three one-run games this season after establishing a Major League record by winning 29 of them last year.
Brian Matusz (2-0) recorded the final two outs in the Boston sixth and became the winning pitcher when the Orioles produce their run in the seventh.
Jim Johnson put the tying run on base with one out in the ninth, but escaped further problems and picked up his fourth save.