Lucien Favre's side cruised to victory against their local rivals, as Frank Schaefer's second spell in charge of the visitors ended in an ignominious defeat
The hosts dominated proceedings in the first period but were only a goal to the good at the break thanks to Juan Arango's strike. After the restart, Tony Jantschke and Marco Reus found the net to give their side a comfortable victory.
Augsburg's victory over Wolfsburg yesterday made victory a necessity for Koln, but it was the hosts who started the game the stronger.
Less than three minutes had passed when Filip Daems swung in a cross towards the far post, and Mike Hanke unleashed a ferocious volley which Michael Rensing did brilliantly to beat away.
Minutes later, Lucien Favre's side had claims for a penalty turned down. Martin Stranzl and Milivoje Novakovic were involved in a tangle of legs after an Arango corner, and although the Austrian's fall was theatrical, he was perhaps unlucky to have his pleas ignored.
However, it was not long before Gladbach got their goal. Martin Lanig brought down Marco Reus on the edge of the box, and Arango stepped up and curled the resulting free kick past Rensing's outstretched hands.
The former Bayern Munich goalkeeper was in for a busy afternoon, and shortly after the goal, he was forced to tip a miscued Reus volley over the bar.
The pressure continued, with Christian Eichner making a great challenge to stop Havard Nordtveit from doubling the lead after the Norwegian burst through the Koln defence to latch onto a Reus through ball.
Gradually, however, Koln began to inch their way back into the match. Lukas Podolski had already sent an ambitious effort well over the bar before Novakovic inexplicably lazed Christian Clemens' cross-shot over from two yards.
Soon after, Novakovic brilliantly flicked on Clemens' corner at the near post, but no red jersey was there to apply a finishing touch and bring their side level.
In the end, Koln almost gifted Gladbach a second. Henrique Sereno succumbed to some heavy pressure from Reus, and fed Hanke, whose strike was blocked by Rensing when he should have done far better.
Having been static in the first half, the visitors came out for the second half in pursuit of an immediate equaliser.
Marc-Andre ter Stegen was called into his first meaningful save of the afternoon, tipping a powerful strike from Clemens behind, and after a goal-mouth scramble from the resulting corner, neither Podolski nor Novakovic were able to prod the ball home.
However, they soon fell even further behind. Reus swung in a free kick from the left, and Tony Jantschke was there to head the ball into the back of the net, despite Rensing's best efforts.
Seconds later, it was 3-0. Reus left a string of Koln defenders in his wake, before prodding the ball into the bottom corner.
From then on, it was little more than a game of keep-ball for the hosts, who seemed able to create opportunities at will. Arango and Reus combined brilliantly to send the Venezuelan clear, but Rensing was there to deny another goal.
As the match entered the final 15 minutes, Rensing was there once more to brilliantly tip a Roel Brouwers header over the bar after the Dutchman emphatically met Arango's cross.
However, in the end, 3-0 was enough for the hosts, who were barely forced to break a sweat, all things told.
This result puts the hosts a point behind Schalke, who currently sit in third place, while Koln's struggle for survival shows no signs of subsiding as Frank Schaefer's men languish four points behind Augsburg.