Hoffenheim, fresh from a 1-1 draw at Borussia Mönchengladbach last weekend, had extended their unlikely unbeaten run to 13 games. In a bid to make it 14, Julian Nagelsmann made three changes. Kevin Vogt, Toljan, Nadiem Amiri replaced Fabian Schär, Steven Zuber and Adam Szalai.
As for Köln, they were locked on 22 points along with their hosts before the game began. Peter Stöger's side had been good value for their spot in the top six, and could have been in the Champions League places had FC Augsburg not held them to a nil-all draw. He made just one alteration from that game as Salih Özcan came in for Marco Höger.
Hoffenheim clinical in front of goal
Overall it was an even opening 10 minutes where both sides enjoyed possession, but the first real chance fell the way of the hosts and they were able to convert. Benjamin Hübner rose highest to meet Sebastian Rudy's corner, only to see it crash off the bar. However, Wagner was quickest to the rebound and fired home from close range.
Yet the Billy Goats would show their fighting spirit as soon as they conceded. Anthony Modeste had a tough opportunity to level from Marcel Risse's cross-field pass, yet his effort sailed well over the bar. Risse himself would benefit from a similar long ball by Simon Zoller. His control was excellent but the finish went narrowly past the post.
Unfortunately for Köln, both Modeste and Risse picked up knocks as they attempted to find the back of the net. The former was able to continue, though their star winger was forced off and replaced by Marcel Hartel. Hoffenheim came forward while the visitors reorganised, yet no-one could convert Andrej Kramaric's clever cut-back.
Hartel almost got his side level when more good work from Zoller found Konstantin Rausch motoring down the left wing. His cross was pin-point, but the youngster couldn't convert on the stretch. Just as Köln looked to be building up a head of steam, Hoffenheim hit them with a sucker-punch towards the end of the first half.
It was a fantastic move from start to finish as Amiri and Toljan fully justified their inclusions in the side. A great one-two mid-way inside the opposition half saw Amiri give-and-go with Wagner, before driving into space. A superb pass cut a route to goal for Toljan to sneak around Frederik Sörensen and finish through Kessler's legs.
Wagner seals the three points
The second half began at a much slower pace compared to the first as both sides remained unchanged after the half-time interval. With Hoffenheim still in control, Nagelsmann made a double change on the hour mark to try and inject life into the game as Baris Atik and Mark Uth replaced Eugen Polanski and Kramaric.
Unsurprisingly, Stöger responded with a double switch of his own. Sehrou Guirassy and Artjoms Rudnevs were thrown into the action for Özcan and Zoller.
However, those changes would matter little in the grand scheme of things as Hoffenheim put the game beyond doubt five minutes later. A searching ball from deep by Uth was met by the towering figure of Sandro Wagner, who made no mistake in powering a header past the helpless Kessler.
To their credit, Köln didn't lose all hope and tried to find a way back into the game late on. Hartel forced the first real save of the afternoon from Oliver Baumann, though his 25-yard drive was relatively comfortable for the experience stopper. Modeste also had a good opening, with his flicked header narrowly over the bar.
The misery would be compounded in the final minute of normal time, as another snappy move saw Toljan get into that left channel once more. With the defence disorientated, a low cross into the near post was finished brilliantly by Uth. The result left Hoffenheim third, as the Billy Goats slipped to seventh.