- Donyell Malen (88')
The Dutchman snatched the winner after a lacklustre performance by the hosts, who last season failed to win their first league title in 12 years after slipping up on the last matchday.
Dortmund were in control but hardly managed to get into the Cologne box.
"Today there was not a lot of things that we liked," said Dortmund coach Edin Terzic. "We take the three points with us. It was not a good performance."
"We had to handle a lot of counter attacks because our centre was completely open. There was also some luck that Cologne did not convert their situations."
The visitors had their best chance in the first half with Davie Selke's deflected shot that bounced off the cross bar.
There was little to cheer for the sold-out 81,000 crowd in the stadium, with Dortmund finding no way past a disciplined Cologne defence for much of the game, even after coach Edin Terzic replaced his entire frontline in the second half.
But Malen broke the deadlock, volleying in at the far post after Felix Nmecha had headed on a corner, to give his team a winning start to the campaign.
Champions Bayern Munich kicked off their season with a 4-0 demolition of hosts Werder Bremen on Friday with league record signing Harry Kane scoring one goal and setting up another on his Bundesliga debut.
- Deniz Aytekin
|1. FC Heidenheim 1846||14||4||2||8||-9||14|
|1. FC Union Berlin||13||3||1||9||-13||10|
|SV Darmstadt 98||14||2||3||9||-20||9|