Second-placed Bayern, the defending champions, had trimmed Dortmund's lead to three points on Friday with an impressive 3-1 win at Hoffenheim as Leon Goretzka scored two superb first-half goals.
Maurizio Sarri's men risk being caught after a fourth defeat in 11 league matches that underlined the need for a striker, as the club close in on signing Gonzalo Higuain on loan from Juventus.
The other semis lineup will feature Al Kharaitiyat and Al Gharafa.
With second-placed Manchester City travelling to bottom of the table Huddersfield on Sunday, Liverpool seized the chance to tighten their grip on the title race.
Pogba opened the scoring by winning and converting a spot-kick for his 10th United goal of the season –- equalling his best club total in a single campaign.
El Shaarawy fired in the winner midway through the second half after coming on as a substitute in the sixth minute for injured Turkish winger Cengiz Under and watching his side throw away a two-goal half-time lead in the second period.
Madrid began the day 10 points adrift of leaders Barcelona, a gap that will be restored if the Catalans defeat Leganes on Sunday, but this victory should inject a timely shot of confidence.
Although Sunday's last-16 game could go to penalties, Lippi, 70, said there was little point practising spot-kicks, and that he hadn't yet decided who would take them.
Leeds lead the Championship, England football's second tier.
Reus is Dortmund born and bred, having come up through their youth academy, and is in great form on the left wing, with 11 goals in 17 league games for the league leaders ahead of their clash with RB Leipzig on Saturday night.
Nuno Espirito Santo's side blew a two-goal lead and then wasted a 3-2 advantage, but still finished with all three points in one of the Premier League's games of the season at Molineux.
The move comes despite guiding the Matildas to as high as fourth in the FIFA world rankings in one of their most successful eras since being appointed in 2014.
French-born Koulibaly was targeted by monkey noises and racist chants in Napoli's 1-0 defeat to Inter Milan at the San Siro on December 26, before being sent off for sarcastically applauding referee Paolo Mazzoleni.
Dortmund face fourth-placed RB Leipzig away on Saturday night.
#Gharafa overcame the challenge of Al Ahli in the other quarterfinal