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 in a row 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.
Sean Monahan scored for the Blue Jackets (22-20-7), who had won their first three games under Bowness after replacing Dean Evason on Jan. 12. 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.
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.
Monahan tied it 1-1 at 7:46 from low in the right circle off a backhand feed by Boone Jenner.
Stutzle put the Senators back ahead 2-1 at 10:15. He skated up from the right goal line to the left circle before scoring five-hole.
Greig made it 3-1 at 6:49 of the third period on an odd-man rush after a giveaway at the attacking blue line by Ivan Provorov. It was Ottawa’s first shot on goal of the period.
Tkachuk then scored an empty-net goal off an assist from Stutzle at 16:54 for the 4-1 final.
