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.
"Guys are working really hard," Blue Jackets coach Todd Richards said. "They earned all the points that we've gotten over the past six, seven games or whatever it is."
Four of the five wins in their streak have come either in overtime or a shootout.
Columbus went 4-0-1 in the season series with Detroit.
"They've been giving it to us. It's great to come back strong," Brassard said.
It will likely be the last divisional game between the teams because of the NHL's proposed realignment plan that could be in effect next season. Both the Blue Jackets and Red Wings would move to the Eastern Conference but to different divisions.
"It definitely is frustrating we couldn't pick up the second point there, but on the bright side we still got one," Howard said. "They're tough. They play a tough style. They dump the puck in and then they all fall back in their own zone. All five of them are just standing there in front of the net, and it's tough to get pucks through."
Franzen tied it 2-2 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.
"If you give them, with their skill players, that much time on a 5-on-3, they're going to capitalize," Johansen said.
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.
"It's pretty hard to play here, especially back-to-back," Brassard said. "We just had to find a way to get off to a good start. That was the key to the game, the first 10 minutes."
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.