Derick Brassard and R.J. Umberger had goals in regulation, and Sergei Bobrovsky made 20 saves through overtime for Columbus, which has won five straight. The Blue Jackets topped the Red Wings 3-0 in Columbus on Saturday.
The Blue Jackets are 5-0-2 in their last seven games after getting only 12 points in their first 19.
Jakub Kindl and Johan Franzen scored for Detroit in regulation, and Jimmy Howard stopped 19 shots. Pavel Datsyuk scored the Red Wings' only goal in the shootout.
Franzen tied the game at 2 with a 5-on-3, power-play goal 25 seconds into the third period. Franzen fired a one-timer from the inside edge of the right circle off a pass from Damien Brunner for his fifth goal.
Johansen was already in the penalty box for slashing when on the ensuing faceoff, Umberger handled the puck with his hand in the final minute of the second period.
The first three goals of the game were scored in a 1:15 span early in the second period, and the Blue Jackets held a 2-1 lead after the flurry.
Brassard opened the scoring 3:10 into the second when he beat Howard with a slap shot from the top of the right circle for his fourth goal. Kindl tied it with his third goal 30 seconds later when he beat Bobrovsky from just above the high slot with a slap shot.
Umberger capitalized on Zetterberg's turnover and ripped a slap shot past Howard from the top of the right circle to give Columbus the lead. It was Umberger's fifth goal.
Columbus outshot Detroit 6-4 in the first period. The Blue Jackets also continued to effectively forecheck the Red Wings as they did Saturday.
NOTES: Detroit D Ian White returned to the lineup after being a healthy scratch the previous six games. He replaced rookie Brian Lashoff, who was a healthy scratch on Sunday. . Columbus C Artem Anisimov missed his second game because of a lower body injury. . Detroit forward Valtteri Filppula missed his seventh game due to a shoulder injury.