It was the Blue Jackets' fourth straight win, improving coach Ken Hitchcock's record to 5-3-0 after taking over a team that was 5-13-2.
Christoph Schubert and Mike Fisher picked up the Senators' goals, both in the third period.
Ottawa, which lost its third in a row, had not given up more than two power-play goals in a game this season. The five goals with a man advantage for Columbus tied the Senators' franchise record for an opponent.
Columbus defenceman Ron Hainsey had a goal and two assists for his first career three-point game in his 115th NHL contest. David Vyborny and Anders Eriksson each added two assists for the Blue Jackets, who had their most goals this season. Manny Malhotra also scored his first goal in 23 games.
Goaltender Pascal Leclaire had a stellar outing with 19 saves before leaving with a 5-0 lead late in the second period. On an Ottawa rush, he stretched to kick aside a shot and was unable to get back up.
He stopped Peter Schaefer on two breakaways and turned him away on a second-period penalty shot.