Werenski scored to extend his home point streak to 19 games, and Dante Fabbro also scored for the Blue Jackets (24-19-7), who had lost three of four. Merzlikins made 31 saves.
Columbus has won five straight home games.
“We have one goal in mind right now and that's to get into playoffs,” Fabbro said. “We're all pulling the same rope, focusing on the present, and treating every game like it means everything.”
Phillip Danault scored, and Kevin Fiala had two assists for the Kings (26-14-6), who have lost five of seven. Kuemper made 21 saves.
“A game we should have won,” Los Angeles coach Jim Hiller said. “I thought we deserved to win, but we've had games like that. We've pulled the rabbit out of the hat before. Satisfied. We had a really good 6-on-5. Got one point. This is not what we wanted, but we'll take it and move on.”
Werenski gave the Blue Jackets a 1-0 lead at 9:24 of the first period with a wrist shot to the upper-right corner from the left circle.
His 19-game home point streak tied John Van Boxmeer (1981-82) for the fifth-longest run by a defenseman in NHL history. Werenski has 36 points (13 goals, 23 assists) during the streak.