Cologne made what could prove to be a decisive step away from the Bundesliga relegation zone with a 3-2 win over Hoffenheim, who wasted another opportunity to move into the top six.

Matthias Lehmann and Anthony Ujah gave Cologne a two-goal advantage before a red card for Pawel Olkowski and penalty from Eugen Polanski set up a grandstand finale.

Despite having only 10 men, Cologne restored their two-goal advantage through Jonas Hector, but an Anthony Modeste goal late on made things interesting once again.

Nevertheless, Peter Stoger's men held on for all three points, moving them six points clear of the bottom three with six games of the season remaining.

Hoffenheim came into the game having seen their DFB-Pokal dreams shattered by Borussia Dortmund in midweek, but knowing a win would boost their hopes of qualifying for Europe next season in view of Augsburg's defeat to Paderborn on Saturday.

They started strongly, but gave their hosts the chance to take the lead in the 20th minute when Ermin Bicakcic fouled Yuya Osako inside the penalty area.

Captain Lehmann got rather lucky as his spot-kick passed through the legs of Oliver Baumann, but it crucially went in to give Cologne the lead.

Ujah should have doubled Cologne's lead before the break, but he struck the post from just a yard out, wasting a glorious opportunity for the hosts.

He took his and Cologne's next chance 10 minutes into the second half, beating Baumann in a one-on-one situation after receiving the ball from Osako's finely weighted pass.

Cologne's lead was reduced 15 minutes later when Olkowski brought Modeste down inside the area. Not only did the referee award a penalty, he also showed the Pole the red card, judging it to be a foul as the last man.

Polanski made no mistake from the spot, bringing Hoffenheim back into the game with 20 minutes remaining.

Cologne got men behind the ball to defend their advantage, but Hector was keen on doing more than just defending as he burst past four Hoffenheim players before taking a shot on goal, which took a deflection on its way past Baumann off Bicakcic.

Hoffenheim launched a last, late assault on the Cologne goal and managed to pull a goal back once again with Modeste heading in Sebastian Rudy's corner.

Cologne managed to hold on, though, with a Steven Zuber header the closest Hoffenheim came to snatching a point at the Mungersdorfer Stadion.