Man United boss Jose Mourinho made three changes to the team that started Sunday's 3-0 win over Sunderland in the Premier League. Antonio Valencia replaced Luke Shaw at the back, while Michael Carrick and Marcus Rashford came in for Ander Herrera and Marouane Fellaini, who both dropped to the bench.
As for Anderlecht, the hosts were captained by highly-rated midfielder Youri Tielemans, with the in-demand 19-year-old starting in the middle of a central three. On-loan Bordeaux forward Isaac Kiese Thelin led the line for the Belgian hosts, while there was also a spot in the XI for Frank Acheampong.
Both teams used their pace in the final third to cause problems in the early moments, with Rashford having the chance to run at the Anderlecht defence, and Acheampong testing Valencia's legs in a wide position.
The first shot of the match came from Acheampong in the ninth minute when the speedy winger, who started well, drove to the edge of the Man United box before releasing, but his effort was always moving wide of Sergio Romero's post.
Man United's first real chance of the night came in the 17th minute when Zlatan Ibrahimovic's blocked effort from a Rashford cross fell to Lingard, but the England international could only hit the post from close range as the visitors passed up two big chances to take the lead in Brussels.
Rashford was next to come close for the Red Devils as he continued to impress in the opening 20 minutes, but the teenager's curling effort just missed Ruben Martinez's post as the score remained level.
Man United had two more chances just before the 30-minute mark when Rashford and Mkhitaryan both released goal-bound strikes, but Serigne Mbodji and Bram Nuytinck took it in turns to make important blocks.
Mourinho's side were purring, however, and they deservedly made the breakthrough in the 37th minute when Mkhitaryan converted from a wide angle after Ruben had got down well to keep out a testing strike from Rashford, whose pace caused the hosts all sorts of problems in the opening 45 minutes.
Nicolae Stanciu had the chance to threaten Romero from a 25-yard free kick early in the second period, but the number 73's effort was always rising over the Man United crossbar, before Valencia was forced to turn off his own line after Massimo Bruno's deflected effort had beaten Romero.
Anderlecht continued to cause problems in the early stages of the second period, with Tielemans, Acheampong and Thelin all more involved after a difficult first half against the 20-time English champions.
Man United came close to doubling their lead in the 55th minute when Matteo Darmian picked out Mkhitaryan's boot with a brilliant cross from the left, but the Armenian's volley just dropped wide of Ruben's far post.
Ivan Obradovic had a decent opening for Anderlecht just before the hour after finding space inside the Man United box, but the defender's effort was wide of the post as the visitors kept their one-goal lead intact.
Anthony Martial for Lingard was Man United's first change in the 63rd minute, although chances were few and far between as the match entered its final 20 minutes with Mourinho's side still boasting a narrow advantage.
Fellaini joined Martial off the Man United bench for the final 15 minutes, while there was also an appearance for Anderlecht's leading scorer Lukasz Teodorczyk as the hosts looked to hit back late on.
Sofiane Hanni had a decent chance for the home side 10 minutes from time when he worked some space outside the Man United box, but the number 94's effort was deflected wide of Romero's post, before Fellaini stung the palms of Ruben down the other end of the field.
Pogba had a glorious opportunity to double Man United's lead in the 83rd minute after being released by Ibrahimovic, but the Frenchman could not find a route past Ruben in the Anderlecht goal.
The visitors incredibly levelled the scores in the 86th minute, however, when Dendoncker jumped above Darmian to head a brilliant Hanni cross into the back of the net, and that was how it finished in Brussels.