Paul scored his first of the season when his soft shot hit the tip of Bobrovsky's stick blade and the puck went in between his skates.
"I saw [Nate] Thompson driving the net, so I just threw it at the net and it ended up going in off his stick," Paul said. "It was a nice feeling to give the team a little momentum and we came back hard."
"I've never scored one like that, but it's nice to have the bounce go my way there."
Duchene then tied it on a breakaway, deking to his backhand for his seventh of the season.
Stone gave the Senators the lead with his 15th of the season when he jammed the puck by Bobrovsky's pad at the left post. Ryan took a pass from Karlsson and scored from the slot to the glove side.
"After they scored those two goals at the end of the second period, it gave them life," Werenski said. "We just didn't come out strong in the third period and they did. We talked about it between periods, that it's going to happen, it's a tied hockey game and the next one's huge and we didn't elevate our game so it's kind of our fault, I think."
The Blue Jackets lost a two-goal lead for the second game in a row; they did it three times at the Pittsburgh Penguins on Wednesday and lost 5-4 in a shootout.