Poland striker Robert Lewandowski's 44th-minute strike proved to be enough to give Dortmund their 19th win of the season from 25 games.
With nine matches left to play, Jürgen Klopp's team are cruising towards their first league title since 2002 and a Champions League place next season.
"This was probably one of the most deserved 1-0 wins of all times," said Klopp after his side laid seige to the Cologne goal in the second-half. "The boys created so many chances over the 90 minutes. The fact that things worked out this way is unbelievable. The team is continuing to take these little steps (towards the title)."
"Robert Lewandowski is a great lad, I am sincerely pleased for him that he scored the winner, that is another feather in his cap," he added.
Second-placed Leverkusen have a chance to close the gap when they host Wolfsburg on Saturday evening, while defending champions Bayern Munich, fourth, badly need a win at third-placed Hanover after back-to-back defeats.
Dortmund's Lewandowski opened the scoring when he chested down the ball from a long pass and slammed it into the bottom far corner just before the half-time break to put his team in control.
Despite missing last week with a knee injury, Dortmund goalkeeper Roman Weidenfeller produced several good saves, especially in the first-half, to keep Cologne out.
Dortmund's reserve goalkeeper, Australian Mitchell Langerak who produced a stellar performance in Munich last week in the 3-1 win over defending champions Bayern, was relegated back to the bench.
Cologne's ex-Bayern goalkeeper Michael Rensing had a busy second-half as he denied Lewandowski, only for Dortmund striker Lucas Barrios to then hit the cross-bar - for the eighth time this season - with less than 15 minutes left.
Bayern begin their recovery after the shock of Wednesday's 1-0 defeat at home to Schalke, in the semi-final of the German Cup, at Hanover on Saturday after last weekend's league defeat at home to Dortmund.
Coach Louis van Gaal has acknowledged a third straight defeat may cost him his job - less then a fortnight after his team won at holders Inter Milan in the Champions League.