Salomon Kalou's missed spot-kick put hosts Borussia Dortmund into the German Cup quarter-finals on Wednesday as Hertha Berlin lost 3-2 on penalties after a 1-1 draw.

The Ivory Coast striker gave Hertha a first-half lead in the third-round cup clash in Dortmund when he volleyed home on 27 minutes after the hosts made a slow start.

But Dortmund raised the pace as Marco Reus equalised straight after the break while Pierre-Emerick Aubameyang had a goal disallowed and Ousmane Dembele fired wide for Borussia.

Dortmund kept up the pressure as the game went into extra time.

However, they finished with 10 men when defender Sokratis was sent off in the 119th minute for dissent -- just before the final whistle -- as his back-chat earned him two yellow cards in quick succession.

In the shoot-out, goalkeeper Roman Burki was Dortmund's hero.

He saved Hertha's second penalty from Vladimir Darida and stopped Sami Allagui's fourth shot, although unluckily for Burki the ball still rolled into the net.

But Kalou blasted his effort over the bar to send Dortmund through.

Before kick-off, Dortmund captain Marcel Schmelzer addressed home fans to criticise hooligans who attacked RB Leipzig supporters, including families, before Saturday's home league game.

The violence has shocked Germany.

"We as players were, and are, very shocked at what happened," said Schmelzer in a video message.

"On Saturday, people were harmed and we condemn that as a team.

"We, the team, wish all victims a good and speedy recovery and apologise for what happened."

Eintracht Frankfurt also reached the quarters with a 2-1 win at second-division Hanover 96 with goals from Israel defender Taleb Tawatha and striker Haris Seferovic.

Schalke saw off second-division Sandhausen with a 4-1 win thanks to three goals in a devastating seven minute-spell from Alessandro Schoepf, Daniel Caligiuri and Naldo.

Third-division minnows Sportfreunde Lotte, from near Osnabrueck, continued their giant-killing run with a 2-0 win at home to second-tier 1860 Munich.

A heavy snowfall had threatened to delay kick-off, but goals by midfielder Jaroslaw Lindner and striker Kevin Freiberger sealed the win.

It was another scalp for Lotte having already beaten top-tier clubs Werder Bremen and Bayer Leverkusen in the previous rounds.

On Tuesday, holders Bayern Munich reached the quarter-finals for the 10th year in a row with a 1-0 win over Wolfsburg, thanks to some heroics from goalkeeper Manuel Neuer.

Bayern were coasting at Munich's Allianz Arena after a well-taken goal from Douglas Costa on 17 minutes, but two superb saves from Neuer denied Yunus Malli.

Borussia Moenchengladbach reached the quarters with a 2-0 success at second-division Greuther Fuerth thanks to goals by Oscar Wendt and a Thorgan Hazard penalty.

Hamburg brushed off poor Bundesliga form to win 2-0 at home to Cologne with goals by Gideon Jung and US striker Bobby Wood.

Second division Arminia Bielefeld are into the last eight after a scare against fourth division minnows Astoria Walldorf, progressing 5-4 on penalties after a 1-1 draw.