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.
Leipzig see off Wolfsburg to reach German Cup semis
Yussuf Poulsen and Hwang Hee-chan netted second-half goals as RB Leipzig beat Wolfsburg 2-0 in the German Cup quarter-finals on Wednesday, while second-tier Holstein Kiel also reached the last four.
The other quarter-final tie was postponed on Tuesday as Bundesliga 2 club Jahn Regensburg were quarantined after a Covid-19 outbreak before their home tie against Werder Bremen.
Hosts Leipzig, who are second in the Bundesliga, shaded visitors Wolfsburg who are one place below them in the league table.
"We fought hard and made it clear we wanted the win, even though the lads have a few games in their bones," said coach Julian Nagelsmann, with Leipzig hoping to repeat their run to the 2018/19 final.
Wolfsburg squandered a first-half penalty when Dutch striker Wout Weghorst slipped and skied his spot-kick over the bar.
Leipzig had the ball in the net moments later but Justin Kluivert's effort was ruled out with Christopher Nkunku offside.
The hosts got the breakthrough when Poulsen shook off his marker and fired into the bottom corner on 63 minutes.
Hwang made sure of the victory two minutes before the final whistle when he tapped home the rebound after Emil Forsberg had a shot saved.
Earlier, Holstein Kiel, who knocked out Bayern Munich in the second round, reached the semi-finals for the first time with a 3-0 win at fourth-division Rot-Weiss Essen.
Holstein took command with two goals in as many first-half minutes behind closed doors in Essen.
Alexander Muehling converted a penalty on 26 minutes before former Bremen midfielder Fin Bartels put in a long header to the far post two minutes later where Janni-Luca Serra tapped the ball in.
Bartels' replacement Joshua Mees added Kiel's third goal in the 90th minute when his shot was deflected into the Essen net.
The semi-finals will be held on May 1/2 with the final scheduled for May 13 at Berlin's Olympic Stadium.
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