Oliver Bjorkstrand, David Savard and Cam Atkinson scored for the Blue Jackets (14-15-8), who were coming off back-to-back losses to the Detroit Red Wings on Saturday and Sunday.
"These kinds of games are going to help me go where I want to go, which is up," Merzlikins said. "We played much better. Like I said before, I think the great thing with the day off after the bad weekend was that we could clear our mind and change our mentality right away. But this is only one game. We haven't won anything. We have to keep focusing."
Mathieu Joseph scored, and Curtis McElhinney made 18 saves for the Lightning (24-9-2), who lost three straight games for the first time this season.
"If there was one issue to our game it's that we let the goalie see everything," Tampa Bay coach Jon Cooper said. "We were doing a lot of good things. The process was fine, we had our legs. We just didn't take eyes away. We had our looks, just tonight they didn't go in."
Bjorkstrand gave Columbus a 1-0 lead at 10:49 of the second period with a redirection of a shot by Zach Werenski.
"It's a big two points," Bjorkstrand said. "Honestly, we're in a situation where we've got to win. We had more of a mindset of winning battles and simplifying things a little bit."