It was the first time for 27 years Bayern have conceded so many goals so early in any competition.
Hoffenheim handed out a 5-1 thrashing to second division Holstein Kiel.
Wolfsburg used six substitutions rather than the permitted five in the game on 8 August.
Bayern Munich's German Cup tie against Bremer SV postponed; doubts in Borussia Dortmund after COVID-19 cases
The first round of the German Cup will take place without Bayern Munich, after the squad of Bremen-based opponents Bremer SV were quarantined for 14 days as three players tested positive.
RB Leipzig face either Borussia Dortmund or Holstein Kiel, who knocked out Bayern Munich, in the final on 13 May.
Inter Milan could secure a first Serie A crown since Jose Mourinho led the club to the treble in 2010 if they win and Atalanta drop points at Sassuolo on Sunday.
German Cup: RB Leipzig through to semis with victory over Wolfsburg; Holstein Kiel also reach last-four
After Poulsen opened the scoring, South Korea striker Hwang came off the bench to hit a late second goal and seal a semi-final berth alongside Borussia Dortmund and Kiel.
Sancho slotted home the winner after the visitors launched a counter-attack from their own area in the second half of the quarter-final at Borussia Park.
European football matchday: Barcelona host Sevilla in semi-finals of Copa del Rey; Ibrahimovic-less AC Milan play Inter
A look at what’s happening in European football on Wednesday
Pavard's close-range tap-in was enough to give European champions Bayern their sixth title in quick succession.
Bundesliga side Cologne looked to be cruising into the last eight with 21 minutes gone in the Bavarian town of Regensburg thanks to goals from Ismail Jakobs and Emmanuel Dennis.
Rot-Weiss Essen struck twice in extra time to knock Leverkusen out with a 2-1 defeat.
German Cup: Bayern Munich knocked out of tournament for first time in 20 years by second-division team Holstein Kiel
Bayern led twice but allowed Kiel to equalize for a second time and make it 2-2 in the 90th minute. After extra time, Fin Bartels converted the winning penalty to give Kiel a 6-5 win in the shootout.
Four Wolfsburg players missed out after positive coronavirus tests. Three more were in isolation because of close contact with their infected teammates. Coach Oliver Glasner named three reserve goalkeepers among his seven substitutes, with two of the keepers dressed as outfield players.
Dynamo Dresden sold 72,112 tickets for the German Cup game against Darmstadt. It was more than double the capacity of Dresden's stadium. Dynamo offered fans the “ghost tickets” for five euros as a way to raise funds
DFB-Pokal: Jadon Sancho scores in Borussia Dortmund's win over Eintracht Braunschweig; Schalke beat Ulm
Borussia Mönchengladbach eased past fourth-tier Elversberg 5-0, Darmstadt won at Dynamo Dresden 3-0, and Union Berlin striker Taiwo Awoniyi struck the post with the last kick of the game in a 3-2 defeat at home to second-division Paderborn.
German Cup: Jude Bellingham scores on debut as Borussia Dortmund thrash MSV Duisburg; Dresden beat Hamburg
Dortmund’s task was made easier when Duisburg defender Dominic Volkmer was sent off for chopping down Erling Haaland in the 38th minute.
DFB-Pokal draw for 2020-21 season goes ahead despite missing teams due to coronavirus-enforced delays
Bayern Munich’s title defense of German Cup will begin against one of four teams from the Middle Rhein wine-making region in western Germany – Alemannia Aachen, FC Düren, Viktoria Arnoldsweiler or FC Pesch.
It was Bayern’s second straight league and cup double, their 13th overall. Now Bayern are targeting the reorganised Champions League in August as their bid to repeat the treble-winning season under Jupp Heynckes in 2013.
DFB-Pokal: Robert Lewandowski's winner takes Bayern Munich to final with narrow win over Eintracht Frankfurt
Bayern Munich will face Bayer Leverkusen in the final on 4 July in Berlin.