"Keep playing the game plan, keep putting as many pucks to the net as we can, and hopefully [10 goals in two games] is what we needed to break things open," Dubinsky said.
Tavares gave the Islanders a 1-0 lead with a power-play goal with 2:09 left in the first period. It was his 29th goal of the season and 600th NHL point.
Bjorkstrand scored a power-play goal at 6:02 of the second period to tie the game 1-1. It was the Blue Jackets' 33rd shot on goal.
"First period, shots from everywhere, and we were down 1-0," Columbus coach John Tortorella said. "We just stayed with it, we scored a couple of huge goals on our power play. ... The past couple nights, the pucks have gone in for us."
It was the sixth time in eight games the Islanders have allowed at least 40 shots on goal.
"It's disappointing," New York forward Cal Clutterbuck said. "There isn't a guy in this room that doesn't want (to win). ... They had [26] shots in the first period, they had a couple of power plays, shot the puck a lot on the power play and at 5-on-5. Everyone wants to make a story out of that, but at the end of the day, it was a 1-1 hockey game with a couple minutes left in the second period."
The Islanders host the New York Rangers on Thursday and visit the Hurricanes on Friday.
"It all comes down to everybody really wanting it, and I think they wanted it more than we did and they deserved to win tonight," Halak said. "That's the bottom line. ... I think we need more from everybody."