United eased into the quarter-finals after coming from behind to beat the Austrian side at Old Trafford.
Manchester United set up a quarter-final tie with Copenhagen by completing a comfortable aggregate victory over the Austrian outfit.
Match in brief
The visitors were lively in the first half and came closest to scoring first when Andres Andrade's header struck the bar. They did hit the front after the interval, however, thanks to a wonderful curling effort from distance by Philipp Wiesinger.
The LASK lead only lasted two minutes, though, as Jesse Lingard galloped through to slide in the equaliser, and Ole Gunnar Solskjær's side completed the turnaround late on when Anthony Martial latched on to Juan Mata's pass to fire in the winner.
View from the stadium: Tom Kell, match reporter
United may ultimately be through to the quarter-finals with plenty to spare, but LASK deserve enormous credit for such a spirited, front-foot display. They'd left themselves far too much to do, though, and it's the Premier League side who go through with victory on the night to boot. Next up are Copenhagen in Cologne on Monday. Solskjær's men are bound to go up a gear or two from this and will be one of the teams to beat in Germany.
Jesse Lingard, Manchester United midfielder: "They made it difficult in the first half. They came with nothing to lose but we stuck to the game plan. We knew there was a lot of space in behind to exploit. We were patient but we also had that urgency to go and win the game. That was very important. As soon as we got back level, I felt we could push on from that.
"You can't beat that winning feeling and lifting silverware so it will be a great experience to win a trophy. With the personnel we've got in the squad and the management team behind us, I feel very confident."
• Manchester United are unbeaten in their last 14 UEFA Europa League knockout phase matches.
• Manchester United have only failed to score in one of their last 24 UEFA Europa League games.
• Manchester United have conceded just six goals in their last 13 UEFA Europa League knockout phase matches.
• Manchester United have scored in their last 20 games and have struck two or more in 15 of those matches.
• LASK have scored the first goal in four of their five UEFA Europa League away matches this season.
Manchester United: Romero; Fosu-Mensah (Mengi 84), Maguire, Bailly, Williams (Chong 72); McTominay, Fred (Pereira 64); Mata, Lingard (Pogba 63), James (Martial 84); Ighalo
LASK: Schlager; Andrade (Filipović 80), Wiesinger (Sabitzer 73), Trauner; Ranftl, Michorl, Holland, Renner; Frieser, Raguz, Balić (Reiter 66)
United face Copenhagen in Cologne at 21:00 CET on Monday for a place in the semi-finals.