The pressure on Borussia Monchengladbach coach Jos Luhukay increased on Saturday after a late home defeat to fellow newcomers Cologne made it four losses on the bounce.
Milivoje Novakovic struck home a curling free-kick two minutes from time to snatch the win, when it looked as though Roel Brouwers's 10th-minute goal to cancel out Fabrice Ehret's early effort was enough for a point.
Monchengladbach remain rooted to the bottom of the table on three points, while Cologne's second successive win means they jump to ninth.
The heavy traffic around the Borussia Park stadium delayed Cologne's arrival and the kick-off was put back 10 minutes, but it did not prevent them making a stunning start.
Gladbach goalkeeper Christofer Heimeroth was unable to collect a long bouncing shot by Nemanja Vucicevic in the fifth minute and Ehret pounced to loop the ball home.
Luhukay's men equalised just five minutes later when Brouwers slotted home a loose ball after Filip Daems's header was saved.
The hosts almost took the lead in the 26th minute but Karim Matmour's pass just eluded Rob Friend, while at the other end Vucicevic headed narrowly wide.
Novakovic missed two more opportunities early in the second half but finally struck late on, sending a curling free-kick from just outside the area over the wall and into the left corner, despite Heimeroth getting a hand to it.
