Looking to bounce back from their disappointing defeat to relegation-threatened St. Pauli, the highly motivated hosts started the contest full of intent and should have taken a second-minute lead through Deniz Undav, who saw his attempted chip thwarted by Marvin Schwabe.
Undav's decision to go for the chip rather than a low effort was soon forgotten, as Stuttgart hit the front with a well-worked move that opened up the Koln backline.
Chris Führich’s inch-perfect lofted pass found Jamie Leweling, who nodded the ball down for Demirovic to slot home.
After being pushed onto the back foot, the visitors grew into the half and created the opening for Jan Thielmann to take aim at goal, but he could only fire straight at the grateful Alexander Nubel, ensuring Stuttgart took a lead into the break for the third time in 11 home league games.
With his side looking to restore parity, experienced striker Marius Bulter was presented with the opportunity to hit back before the hour mark, receiving the ball just outside the six-yard box before sending his shot wide to the relief of the home support.
The visitors finally found their radar just shy of the 80-minute mark when Ragnar Ache took full advantage of Jeff Chabot’s misplaced pass.
Luca Waldschmidt quickly latched onto the loose ball before feeding the Koln marksman, who cleverly avoided a challenge and calmly lifted his shot over Nubel.
Demirovic ultimately spared his teammate’s blushes, producing a first-time volley from Ramon Hendriks whipped delivery to swiftly restore Stuttgart’s advantage and take his tally to seven league goals.
Undav joined his fellow forward on the scoresheet in the closing stages, steering a low shot into the bottom corner to make sure of the three points, which take his team into the top four.
As for Lukas Kwasniok’s charges, they remain in 11th, four points clear of the danger zone after seeing their winless away league run stretch to seven matches.
Flashscore Man of the Match: Ermedin Demirovic (Stuttgart)