Lotte were down to 10 men from the 79th minute with the score at 1-1 but they refused to buckle and snatched a memorable victory over top flight Leverkusen after the game finished 2-2 following extra time.
Hamburg SV, without a win in the Bundesliga this season, got a boost from their 4-0 demolition of third division Hallescher FC with United States striker Bobby Wood netting twice.
Hertha Berlin also advanced with a 2-0 win over St Pauli while Borussia Moenchengladbach found little resistance as they beat second division VfB Stuttgart by the same score, Fabian Johnson netting once and setting up the other for Lars Stindl.
Freiburg, however, suffered the same fate as Leverkusen, losing 4-3 in a shootout at home to second division Sandhausen.
Champions League club Leverkusen, who have slipped to 11th after losing their last two Bundesliga matches, were desperate to beat a Lotte side who stunned Werder Bremen in the previous round.
Leverkusen, with coach Roger Schmidt banned for two matches following a verbal attack on his Hoffenheim counterpart in their 3-0 weekend home league loss, struck after 26 minutes when Kevin Volland fired home despite the attentions of two defenders.
The visitors were lucky to keep the lead when a Lotte effort was controversially ruled offside minutes later, but the hosts scored right after the break when Leverkusen's Roberto Hilbert, completely alone, deflected a harmless cross into his own goal.
Lotte's Tim Wendel was then sent off before Volland struck again in the first half of extra time with a close-range volley.
However, the home side refused to give up and came back once more through Kevin Freiberger's equaliser before keeping their cool to claim a famous victory in the penalty shootout.
(Reporting by Karolos Grohmann; Editing by Ken Ferris)
