The win lifts Dortmund into second place in the Bundesliga, with 34 points from 21 matches. Last-place Cologne have just 13 points, reports Efe.
Batshuayi, who joined the German club this week on loan from England's Chelsea, put the visitors ahead with a goal in the 35th minute.
Simon Zoller equalised for Cologne at the hour mark, only to see Batshuayi get his second of the night two minutes later.
The hosts pulled level again in the 70th minute, courtesy of a goal by Jorge Mere, and it began to look like Dortmund were going to drop points yet again.
But with six minutes left in regulation, Andre Sch?rrle put Dortmund up 3-2 for good.
The outcome provided a measure of revenge to Dortmund coach Peter St?ger, who was fired by Cologne at the beginning of December.
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