Berggren put the Blues ahead 4-3 during a delayed penalty after he was tripped by Columbus forward Mathieu Olivier. Colton Parayko threw the puck to the net from below the goal line in front, where Jet Greaves robbed Mason McTavish, but Berggren was there to lift in the rebound from in tight.
Jimmy Snuggerud scored twice, and Dylan Holloway had three assists for the Blues (2-2-1), who ended a three-game skid (0-2-1). Jordan Binnington made 20 saves.
Valeri Nichushkin, Kent Johnson and Cole Sillinger scored for the Blue Jackets (2-2-0), who defeated the Pittsburgh Penguins 3-2 in a shootout at home on Friday. Greaves made 22 saves.
Nichushkin gave the Blue Jackets a 1-0 lead at 16:10 of the first period. Eric Gudbranson drove down the left side of the ice and centered a puck off the side of the net into the slot, where Sean Monahan pounced on it and his shot caught a piece of Nichushkin before going in the net.
Johnson made it 2-0 at 19:48 on a wrist shot from the left face-off circle into the top right corner.
Jake Neighbours cut the deficit to 2-1 at 6:10 of the second period, whacking in the rebound fomr a Justin Barron slap shot.
Snuggerud tied it 2-2 at 9:02 on a backdoor tap-in. Philip Broberg drove the puck wide around Sillinger and found Snuggerud crashing the net after he got behind Zach Werenski.
Snuggerud put the Blues up 3-2 with his second goal of the game at 12:32, collecting a drop pass from Robert Thomas, and firing a wrister from the right circle in off the far post.
Sillinger tied the game 3-3 at 6:51 of the third period from the slot after Binnington gave up a sharp-angle rebound off a Charlie Coyle shot.
After Berggren's goal, Pavel Buchnevich secured the 5-3 final with an empty-net goal at 19:17 of the third period.
