The Orioles were trailing 2-0 in the fourth when Manny Machado drew a leadoff walk from Athletics starter A.J. Griffith and Markakis followed by launching a score-tying, two-run blast. Jones then put Baltimore ahead to stay with a solo blast.
Nate McLouth finished 3-for-5 with a solo homer and two RBI and J.J. Hardy drove in a run for the Orioles, who logged a third consecutive win against the A's.
Chris Tillman (1-1) earned his first triumph of the year, yielding two runs on seven hits over six innings while walking two and fanning seven.
Jim Johnson pitched a scoreless ninth for his 10th save.
Griffin (2-2) allowed four runs on five hits over seven innings, striking out seven.
Josh Donaldson went 4-for-4 with two RBI for Oakland.