Joonas Korpisalo made 26 saves for the Blue Jackets (5-6-3), who are 0-3-1 in the past four games.
"We've got to get ourselves out of it," Columbus coach John Tortorella said. "We need to get back to where we were playing. We will. That's just how the League is. There's no explanation. You lose your game.
"There's a number of guys really squeezing their sticks."
Monahan made it 1-0 at 3:44 of the first period with his first goal in 14 games dating to Oct. 5 against the Vancouver Canucks.
After Johnny Gaudreau forced a turnover, Lindholm got the puck and passed in the slot to Monahan, whose wrist shot went off Korpisalo's glove.
The goal was a relief for Monahan.
"I've been in this league for a long time, you know you're going to go through stretches and not find the net," he said. "You've got to focus on the little things. That's what I tried to do."
Rittich made two saves in five seconds beginning at 14:22 of the first on a wrist shot by Gustav Nyquist and a shot from the right point by Vladislav Gavrikov.
"It's part of my job. I'm trying to help the guys out," Rittich said.
Coming off a 4-3 overtime loss at the St. Louis Blues on Friday, the Blue Jackets expected a better first period.
"The real tale of the game, honestly, was our start," Columbus captain Nick Foligno said. "For whatever reason, we have a difficult time in our own rink setting the tone in how we want to play. That was the difference."
Bennett scored to make it 2-0 at 8:20 of the second period.
