Schalke's Max Meyer, centre, celebrates his goal against Cologne with Amine Harit, left, and Naldo on Tuesday night. Photo: Martin Meissner/AP

BERLIN – Schalke 04 beat ailing Cologne 1-0 on Tuesday to reach the German Cup quarter-finals, while VfB Stuttgart went out 3-1 at Mainz 05 after failing again to convert a penalty.

Wolfsburg needed extra time to prevail 2-0 at second-division Nuremberg, and third-division Paderborn made the last eight for the first time in a 1-0 win over Ingolstadt.

Schalke broke the deadlock against injury-plagued Bundesliga bottom side Cologne when diminutive Max Meyer seemingly aimed to head on a corner-kick, but the ball sailed over goalkeeper Timo Horn into the far left corner in the 63rd minute.

Horn saved well from Matija Nastasic shortly before the goal and from Breel Embolo with 10 minutes left in the last-16 game, but his teammates were unable to get an equaliser at the other end.

“Things are going very, very well. We have a great team,” said Meyer as Schalke had another reason to cheer after hibernating in second place in the Bundesliga.

Stuttgart led from captain Christian Gentner’s low shot in off the far left post in the 41st.

But Dennis Aogo missed a second when his penalty was saved by Robin Zentner in the 53rd, after Chadrac Akolo had also failed from the spot on Saturday against Bayern Munich.

Mainz levelled from substitute Emil Berggreen’s header off a corner kick in the 62nd, Abdou Diallo – whose handball had led to the penalty – smashed home for 2-1 eight minutes later, and Suat Serdar wrapped up matters in stoppage time.

“We are super happy,” Mainz sports director Rouven Schroeder said, while Stuttgart defender Andreas Beck lamented a host of chances for his team apart from the penalty: “I am lost for words. We simply had to win this game.”

Wolfsburg had Mario Gomez and Divock Origi denied by the post in regulation, but Marcel Tisserand also had to clear an effort from Nuremberg’s Hanno Behrens on the goal-line.

The top-flight side finally went ahead in the 96th when Felix Uduokhai poked home in a goal-mouth scramble. Daniel Didavi wrapped up matters with a low shot in the 118th.

Paderborn meanwhile claimed their third second-division scalp in a row from Ben Zolinski’s 56th-minute strike into the roof of the net against disappointing Ingolstadt.

The other four games are on Wednesday, including the big match between Bayern and holders Borussia Dortmund. The quarter-finals will take place on February 6 and 7.