Jack Roslovic scored, and Michael Hutchinson made 29 saves for the Blue Jackets (23-44-7).
"That's an impressive game for our group," Columbus coach Brad Larsen said. "I really wanted that win for them. They deserved the win tonight. They didn't get it, but that's a hard-fought point."
Roslovic gave the Blue Jackets a 1-0 lead at 8:08 of the first period, tipping in Liam Foudy's backhand cross-ice pass on the doorstep.
"It was an emotional game, physical game; tight checking each way," Columbus captain Boone Jenner said. "That was a good hockey game. Obviously you want to come out and get the two points for that, but like I said, we've got a lot to take from that game."
Bertuzzi tied it 1-1 with a power-play goal at 10:07 of the second period. Pavel Zacha deked around Blue Jackets forward Sean Kuraly and defenseman Marcus Bjork before centering to Bertuzzi at the net front.
Bertuzzi appeared to score again at 13:36, poking the puck between Hutchinson's legs, but the goal was waved off and a video review confirmed the call on the ice that the puck had been frozen prior to it becoming loose.
"We play hard [and] with a lot of effort," Hutchinson said. "Coming down the stretch, we're not going to lay down for anyone and give them space out there just because of where they are in the standings and where we are. So, I don't know if they were expecting us to come out that hard, but it turned into a really good hockey game."