Baltimore thus moved into a tie with the Yankees for the American League East lead. The teams have split the first two games of a four-game series.
The Orioles hit six homers altogether, including a three-run shot by Matt Wieters during a four-run first inning. Robert Andino hit a solo blast in the fourth and Reynolds had one in the sixth while Baltimore was building a 6-1 lead.
New York then sent 10 men to the plate in the eighth with Ichiro Suzuki's two-run single driving in the fourth and fifth runs of the inning to tie it up.
With David Robertson (1-6) on the mound for the Yankees in the bottom of the eighth, Jones hit the fourth pitch of the inning over the wall in left to put Baltimore back in front.
Wieters followed with a single and Reynolds hit a 3-2 pitch out to left to give the Orioles a three-run cushion. Davis hit his homer one out later to finally drive Robertson from the game. Robertson was the sixth of eight New York pitchers.
Darren O'Day (7-1), who threw three pitches to record the final out of the eighth inning, was credited with the win.