The Blue Jackets gave up a game-tying goal with 24.9 seconds to play, but used Ryan Johansen's shootout goal to extend their winning streak to six games in a 4-3 victory over the Buffalo Sabres on Saturday night.
"Every night we have to find a way to get points," said Bobrovsky, who made 26 saves and didn't allow a goal in the shootout.
"That's why we play. It's our goal to be in the playoffs and we have to take points to be there. It doesn't matter how and who we play."
"It's a tough thing to give up a goal in the last minute of the game but this is a group that's faced adversity all season long," Dubinsky said. "And instead of cowering to it and conceding to just one point, we stuck our heads down and went after them.
"I'm really proud of this bunch and the way we stuck together through some adversity."
Myers had two goals for Buffalo, and Drew Stafford also scored.
The Sabres have lost three straight. The Blue Jackets' winning streak matches the longest in franchise history set on April 3, 2006.
"Right now for me it's just a stat," Columbus coach Todd Richards said. "We've done a good job putting ourselves back in the fight and right in the middle of it."
Columbus improved to 24-20-4 after winning just 14 of its first 35 games. Dubinsky said the win streak speaks volumes of his team's improvement.
"It says we're finding ways to win games and we're getting points," Dubinsky said. "We're getting some swagger here and some confidence.
The Sabres struck just 59 seconds into the game when Moulson sent a soft pass across the ice to Myers, who had crept in from the right point and lifted a shot over Bobrovsky to put Buffalo up 1-0.
Columbus countered when a one-time shot from Savard off the right half wall caught Ryan Miller out of position to tie the score at 6:19.
The tie lasted just 28 seconds.
A poor Blue Jackets breakout left Ennis alone in front of Bobrovsky. The Sabres center slid the puck to Stafford at the left post, and he slid it into the open net at 6:47.
"They played a tough game last night," said Ennis, who finished with two assists and seven shots on goal.
"We wanted to jump on them early."
Miller made an athletic save on a 2-on-1 break midway through the first period, reaching behind his body to make a glove save on RJ Umberger. He finished with 32 saves.
The Blue Jackets tied it at 2-2 after a Myers boarding penalty gave them the game's first power play. Calvert whiffed on a backhand attempt, but pushed a second chance past Miller at 12:44 of the first.
Buffalo had a goal disallowed 24 seconds into the second period. Moulson was judged to have used a distinct kicking motion to put the puck behind Bobrovsky.
"The league is screaming for goals and all of a sudden, I don't know how you can kick it and try to stop at the same time," Sabres interim head coach Ted Nolan said.
A power-play goal gave Columbus its first lead at 11:21, as Dubinsky took advantage of crowded Buffalo crease with his rebound goal.
The Blue Jackets needed a right pad save from Bobrovsky on Moulson during a late Sabres power play, but finished the second period with a 3-2 lead.
Buffalo didn't score on its first three power plays, and the last was an abbreviated one when Stafford was hauled down behind the Columbus net with 36.4 seconds to play in regulation.
Nolan called timeout, Buffalo won the faceoff in Columbus zone and Myers sent a wrist shot past Bobrovsky.
Myers almost scored a third goal in overtime, but his low shot went wide of the goal.
Johansen's game-deciding goal required patience. Miller stayed with the third-year man's shootout attempt until an opening appeared just as Johansen reached the crease.
"I thought the play was dead, I really did," Richards said. "When he got there, I thought, 'Oh, he's got nothing' and he got it up quick on his glove side."
The Blue Jackets are off until Tuesday, when they'll host Los Angeles in the first of a three-game homestand.
Buffalo is 6-1-3 in its past 10 home games after beginning the season 3-12-1 at First Niagara Center. They'll next face Florida on Tuesday in the second of three straight at home.
Defenseman Fedor Tyutin was the only scratch for Columbus. ... The game was the 300th of Myers' career. ... Columbus RW Corey Tropp played his first game against the Sabres since Buffalo waived him on Nov. 27.