Brady Tkachuk and Tyler Kleven also scored, and Thomas Chabot had two assists for the Senators (23-19-7), who extended their point streak to five games (3-0-2) after losing two straight in overtime. James Reimer made 21 saves in his second start of the season.
Reimer, 37, signed with the Senators on Jan. 12. He made 30 saves in a 4-3 overtime loss to the Detroit Red Wings on Sunday.
“It's great to get the win,” he said. “I was very thankful, very grateful, as a Christian, grateful to God and just this opportunity.
“And then obviously, the team, being here, it's a lot of fun and the guys tonight I thought they played extremely hard, some huge plays. A couple of pucks slipped behind me and the guys battled hard. So, whenever you win, it's obviously a team thing and tonight it was that in spades.”
Sean Monahan scored for the Blue Jackets (22-20-7), who had won four in a row. Elvis Merzlikins saved five of seven shots in the first period before leaving because of illness. Jet Greaves stopped 12 of 13 shots in relief over the final two periods.
“If you look at the whole 60 minutes, it's probably an evenly played game,” Bowness said. “Our slow start really hurt us. So that's been addressed already. And we'll continue to address that because I hate slow starts. I hate it.
“Again, I think it was an evenly played game for the most part. The start killed us, and more importantly, in the second period, we could have taken the lead, but we didn't score.”
Kleven gave Ottawa a 1-0 lead at 3:34 of the first period with his first goal of the season when he skated to the left dot and snapped a shot to the upper left corner.
“A good game, solid from the drop of the puck. A real good road win,” Senators coach Travis Green said. “We've been much better this season in the offensive zone, controlling the play, controlling the puck.”