May's Stockholm finale is beginning to come into sight after a long, arduous campaign that has undoubtedly taken a toll on their Premier League ambitions.
United's hopes of adding the Europa League to their bulging trophy collection - and securing a Champions League return - remain intact, but there is work to do after Mkhitaryan's first-half goal was cancelled out by a Dendoncker sucker punch as the first leg ended 1-1.
The quarter-final was the fourth successive European trip the Armenian has netted on and Mourinho's relief to return to Old Trafford with an away goal will no doubt be tinged with disappointment after allowing victory to slip away.
First-half endeavour was all too infrequently matched by quality at the small but atmospheric Constant Vanden Stock Stadium, where security was stepped up days on from the Dortmund bomb attack.
Jesse Lingard hit the post on United's first voyage forwards and Mkhitaryan broke the deadlock as half-time approach, turning in from an acute angle after Marcus Rashford was denied during a fine, one-touch move.
Mkhitaryan went close again with a smart volley as Anderlecht first European quarter-final appearance for 20 years looked set to end in defeat, only for lax defending to allow Dendoncker to power home an equaliser.
There was a pleasant atmosphere around the city and stadium despite Tuesday's attack on Borussia Dortmund's team bus increasing the pre-match focus on security.
Armed guards were visible outside the stadium, where fans were prohibited from bringing bags due to concerns over terrorist incidents in a city where 32 were killed during coordinated attacks last March.
Fans were warned to get to the stadium early to go through security checks on a night when United looked comfortable early on as Mourinho plumped for a strong side.
Frank Acheampong and Isaac Kiese Thelin failed with early attempts to throw the visitors off kilter, but such chances became an increasing rarity as they tried to keep it tight.
United were playing the ball around without an edge until Rashford's fine, curling cross fell invitingly for Zlatan Ibrahimovic - a close-range shot denied by Martinez Ruben, with Lingard's unorthodox follow-up coming back off the post.
United were on top from that point and, after Rashford tried his luck from 25 yards, Anderlecht's defence was prised open as pressure paid dividends in the 37th minute.
Ibrahimovic smartly directed Paul Pogba's pass wide to the marauding Antonio Valencia, whose first-time cross was met by a Rashford shot bound for the bottom corner until a fine Ruben save. Unfortunately for the Anderlecht goalkeeper, Mkhitaryan was first to react to the rebound and directed home from a tight angle.
Mourinho punched the air in celebration and smoke soon billowed out of the away end for the second time, leading the stadium announcer to implore United's travelling fans not to use fireworks.
The half-time whistle was timely respite for Anderlecht, with Rene Weiler's men returning for the second half reinvigorated.
Nicolae Stanciu curled a free-kick over from the edge of the box before Valencia dealt with a drive from Massimo Bruno and Acheampong's follow up.
However, Mkhitaryan was close to jolting United from their slumber in style within 10 minutes of the restart, meeting a Matteo Darmian cross with a guided left-footed volley just wide.
Rashford's speculative was dealt with by Ruben and Ivan Obradovic was guilty of wasting a chance at the other end, before getting booked for clattering Rashford.
Alexandru Chipciu's penalty claims were ignored before fellow Anderlecht substitute Sofiane Hanni saw a shot blocked as the match became increasingly scrappy, with Marouane Fellaini seeing an attempt to make himself even more unpopular in Brussels denied.
The towering midfielder saw a header dealt with more comfortably than Pogba's attempt moments earlier - missed chances United were made to rue.
Obradovic was allowed to run down the left and swing in a threatening cross that Dendoncker beat Darmian all too easily to, powering a header past Sergio Romero to send the locals wild and secure a 1-1 draw.