Cologne were crushed 5-0 by Dortmund earlier in the season but there was little sign that a repeat was on the cards when Milivoje Novakovic headed the hosts ahead after 13 minutes.
However, Lukasz Piszczek equalised with another header in the 26th minute, then a spectacular volley from Shinji Kagawa and Robert Lewandowski put Dortmund in control after the break.
A late goal by Cacau gave VfB Stuttgart a 1-0 win over Nuremburg in Sunday's other game between two mid-table sides.
Cologne's shell-shocked players were as baffled by anyone at their second-half collapse.
"We had a chance at half-time but once they made it 3-1, they gave them more room and the played good football," said Sascha Riether. "We have to apologise for our second-half performance."
The hosts made a bright start and went ahead when Novakovic beat two defenders to Martin Lanig's cross to score with a looping header.
Cologne, however, gifted Dortmund an equaliser when Piszczek was allowed to rise unmarked at the near post to head in Marcel Schmelzer's free-kick from near the corner flag.
Kagawa's clever backheel allowed Jakub Blaszczykowski to burst into the area and he laid the ball off for his fellow Pole Lewandowski to convert his 17th goal of the season.
The last quarter-of-an-hour were embarrassing for Stale Solbakken's side who capitulated meekly.
