Jose Mourinho bemoaned his side's lack of killer instinct in front of goal following last week's first leg and it was almost their downfall again as Rashford, Zlatan Ibrahimovic and Paul Pogba all went close in a game in which United had the better chances.

But Rashford, who made his name in this competition last season, scored one goal and made another in a fine display as United ensured their hopes of qualifying for the Champions League through the Europa League continued.

They took a 10th-minute lead when Pogba's excellent through ball found Rashford in space on the left-wing and he cut back for Henrikh Mkhitaryan to fire home from inside the area.

But Anderlecht were level on 32 minutes. Youri Tielemans struck the crossbar with a powerfully hit long-range effort, before Sofiane Hanni reacted quickest to poke the rebound past Sergio Romero from close range.

Ibrahimovic, injured in the final action of added time at the end of the regulation 90 minutes, hobbled down the tunnel to be replaced by Anthony Martial.

United continued to put Anderlecht under pressure without reward before Rashford got on the end of a Marouane Fellaini knockdown to shoot low past goalkeeper Ruben and seal a dramatic win.

Ten-man Ajax turned the tables on Schalke to go through 4-3 on aggregate after a dramatic 3-2 defeat in Germany.

The hosts bagged a pair of goals three minutes apart in the second half to even the tie. Leon Goretzka burst onto a Guido Burgstaller pass before sliding his right-footed shot past Andre Onana in the 53rd minute, before Burgstaller turned scorer and slotted home from the middle of the box after a fine Nick Viergever cross on the left side.

Joel Veltman was issued a second yellow for impeding the progress of Nabil Bentaleb in the 80th minute, putting Ajax down a man.

And Daniel Caligiuri seemingly completed the comeback in extra time with a fine header, climbing over a defender, from Sead Kolasinac's cross in the 101st minute. 

But Ajax fought back with goals from Viergever (111) and Amin Younes (120) to dramatically seal the tie.

Lyon needed penalties to advance past Besiktas, just days after fan trouble forced their Ligue 1 match with Bastia to be abandoned.

Anderson Talisca gave the hosts a lead after 27 minutes, settling a Oguzhan Ozyakup cross in the box, swerving and firing through a forest of legs to beat Anthony Lopes at the far post.

Alexandre Lacazette answered for the visitors seven minutes later with fine goal of his own -- the France international chesting down Maxime Gonalons's long ball just inside the box before smartly chipping the keeper who was left stranded.

But Besiktas and Talisca weren't done, and the Brazilian attacker evened the tie in the 58th with a powerful header of Adriano's cross after leaping over a number of bodies in the box.

After extra time, the match went to penalties, where the teams converted 12 straight attempts before saved attempts on Besiktas' Dusko Tosic and Matej Mitrovic bracketed a miss by Christophe Jallet. Maxime Gonalons, then, sent Fabricio the wrong way on the 16th kick to send Lyon to the next round.

Celta Vigo secured their spot in the next round after a 1-1 draw at Racing Genk put them through 4-3 on aggregate.

Having enjoyed a 3-2 win at home in the first leg, Celta gave Genk all to do after Pione Sisto's opening strike in the 63rd minute.

Leandro Trossard immediately answered four minutes later but the hosts couldn't find the winner before crashing out in the last-eight stage.