United had a 5-0 lead from its first leg played in March and will face Copenhagen which enjoyed a 3-0 victory on the night over Istanbul Basaksehir.
Manchester United edged LASK, while Inter beat Getafe and Inter Milan beat Getafe 2-0 on Wednesday in rescheduled ties due to the coronavirus pandemic to clinch places in the Europa League quarterfinals.
United had a 5-0 lead from its first leg played in March and will face Copenhagen which enjoyed a 3-0 victory on the night over Istanbul Basaksehir.
LASK had to wait until the second half to break the deadlock as defender Philipp Wiesinger rifled into the top corner from outside the box after 55 minutes.
Short-lived
Its celebrations were short-lived as Jesse Lingard equalised on the counter attack for United three minutes later.
Anthony Martial claimed the match-winner with two minutes to go despite LASK goalkpeer Alexander Schlager getting a foot to the France striker’s shot.
Antonio Conte’s Inter Milan will face either Steven Gerrard’s Rangers or Bayer Leverkusen with the Germans holding a 3-1 lead from the first leg.
Romelu Lukaku and Christian Eriksen scored either side of the break for the Italians.
One-off tie
Inter’s meeting with the LaLiga side was played over just one leg in Gelsenkirchen to save time ahead of next week’s last eight to be held in Germany.
It advanced to the next round as Romelu Lukaku became the club’s first player to score in five straight European appearances since Brazilian striker Adriano in 2004.
Lukaku slotted home after Alessandro Bastoni’s long ball after 33 minutes.
The Spaniards were given a chance to take the game to penalties with 25 minutes remaining as VAR said Diego Godin had handballed in his own box but veteran cente-forward Jorge Molina missed the resulting penalty.
Christian Eriksen made sure of Inter’s spot after 84 minutes with his first touch after Dakonam Djene made a mess of a clearance inside his own area.
Important results: Shakhtar Donetsk 3 (Moraes 89, 90+3, Solomon 90+1) bt Wolfsburg 0. Shakhtar wins 5-1 on aggregate.
FC Copenhagen 3 (Wind 4, 53-pen, Falk Jensen 62) bt Istanbul Basaksehir (TUR) 0. Copenhagen wins 3-1 on aggregate.
Manchester United 2 (Lingard 57, Martial 88) bt LASK 1 (Wiesinger 55). United wins 7-1 on aggregate.
Inter Milan 2 (Lukaku 33, Eriksen 83) bt Getafe 0. First leg postponed so played as a one-off tie.