Sean Couturier nearly won it for Philadelphia, but he hit the post on the rush with 17 seconds left.
The Flyers have lost three of four following a six-game winning streak.
"I'm proud of the way the guys played," Elliott said. "There were some big blocked shots, some big plays. [Couturier] could have won it with a couple of seconds left in regulation. Tough bounce."
Jones gave the Blue Jackets a 1-0 lead on the power play at 17:08 of the first period when he scored with a slap shot from the top of the right face-off circle that went off Provorov.
"Off my butt and into the net," Provorov said. "Sometimes stuff like that happens. You try to block the shot, and the next thing you know it changes direction and it's in the net."
Jones, who scored less than a minute after Blue Jackets forward Matt Calvert hit the post on a shorthanded breakaway, has three goals and two assists during a four-game point streak.
Dubois hit the crossbar 3:05 into the second period, and the Flyers took advantage when they tied it 1-1 at 3:56 when Provorov scored off a drop pass from Claude Giroux, who has eight assists during a five-game point streak.
Philadelphia had a goal disallowed with 1:39 left in the second period after video review showed Taylor Leier's stick was over the crossbar when he deflected the puck.
