With the score tied 3-3 in the sixth, Jones and Lew Ford each drew one-out walks from Royals starter Bruce Chen (8-10).
Louis Coleman entered the game and Reynolds greeted him by lining a 2-2 pitch into left field for a solid hit, putting the O's ahead to stay.
Manny Machado socked a two-run homer and Nick Markakis added a solo shot as Baltimore earned a split in its four-game series at Camden Yards.
Chen ended up allowing four runs on four hits over 5 1/3 frames.
Mike Moustakas homered for the Royals.