The Orioles were trailing 3-0 until exploding for seven runs in the seventh.
Shawn Kelley (4-3) relieved, only to allow an RBI single to Matt Wieters, followed by Hardy's go-ahead, three-run shot.
The O's put two more runners and base and Jones then capped the outburst with another homer, this one coming against Joba Chamberlain.
Kevin Gausman (2-3) was credited with the win for the O's, who avoided a three-game sweep. They came into the contest four games out of an American League wild card berth.