Andre Schuerrle made sure of Dortmund's first league win of the year with an 84th minute victor after Cologne twice had come back from a goal down.
Batshuayi, who regularly refers to himself as "Batsman" on social media, has made an instant impression at his new club, having joined Dortmund on an initial loan agreement.
Head coach Peter Stoeger, who was sacked by Cologne in December, threw the Belgian striker in at the deep end to replace Pierre-Emerick Aubameyang. The most important thing is: "We won the game and achieved the three points".
The win moves Dortmund up to second in the Bundesliga, six points behind leader Bayern Munich who have a game in hand.
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"It's my first match, it was always going to be hard, so I am really happy we got the three points". "The victory is good for us and Michy's debut is, of course, fantastic, especially after the weeks of discussion".
Batshuayi was also asked why he signed for Dortmund after the match, to which he replied: "I love Borussia Dortmund". "Since the beginning of the second half of the season I'm in very good shape and can show more and more".
"We want to qualify for the Champions League, and he wants to gain ground when it comes to the Belgian World Cup squad".