Tim Stutzle
scored in the third round for the lone goal of the shootout.
Brady Tkachuk scored in the third period, and
Filip Gustavsson
made 33 saves for the Senators (30-41-7).
"It felt like a little bit of a slow game, the two first periods, like we didn't really play our best game offensively," Gustavsson said. "Then we did pretty good in the third period and we came out of it with the win.
Ottawa is 4-1-1 in its past six games, including a 4-3 shootout win at the Vancouver Canucks on Tuesday.
"As the game went on, I thought we got a little hungrier," Senators coach D.J. Smith. "It was a pretty even game both ways. We just found a way to win."
Jack Roslovic scored, and Elvis Merzlikins made 25 saves for the Blue Jackets (35-36-7), who have lost four in a row.
"It's two young teams trying to battle at it," Roslovic said. "I'm not sure they were the better team tonight."
Roslovic gave Columbus a 1-0 lead at 11:20 of the first period, scoring on a wrist shot off a pass from Cole Sillinger on the power play. He has scored eight goals in his past six games.