The Red Devils produced a professional display to pick up a 1-1 draw in the reverse fixture, seeing them installed as strong favourites to not only progress through but to also go all the way and lift the trophy.
Defeat to Chelsea on Monday night may have signalled just a second loss in 29 outings for United, but it is fair to say that their momentum has stalled since beating Southampton to win the EFL Cup at the end of last month.
A Premier League draw with Bournemouth at Old Trafford a week later, seeing them left frustrated when trying to break down the 10-man Cherries in a fiery affair, was followed up by a 1-1 draw in Rostov-on-Don and that limp 1-0 loss to the Blues when themselves on the wrong end of a big refereeing decision.
It leaves the Red Devils at somewhat of a crossroads, now out of the FA Cup and six points adrift of Liverpool in fourth place, albeit with two games in hand to play on their rivals, following a run of four draws in their last six league outings.
A fourth victory at Wembley Stadium in the space of a year to see off Southampton does certainly offer hope for supporters that Jose Mourinho is the right man to bring long-term success back to the club, with the EFL Cup often a precursor to even better things as far as the Portuguese's recent history in the competition goes.
Mourinho has now openly admitted that the Europa League tops his list of priorities this term, something you certainly did not expect him - or any other top-six manager - to say at the start of the campaign, as this is a competition that is often maligned for the simple fact that it is not the Champions League.
With the carrot at the end of the stick being an automatic spot in Europe's showpiece competition next season, Mourinho knows full well that overcoming four more sides to lift the cup is a more attainable target than overhauling both Arsenal and Liverpool in the race for fourth.
Finishing in, by their standards, a lowly sixth place this term is certainly not how Mourinho will have envisaged his first campaign at the Theatre of Dreams ending, but a domestic cup in the bag and European equivalent potentially to come will be a saving grace.
A quick turnaround in matches this week, seeing them make the trek to Russia for the first leg before taking on Chelsea four days later, could well take its toll come Thursday, though the Red Devils boast a fine record on home soil in European competition - 15 games without defeat now, 12 of those ending in victory.
United did crash out at this stage of the competition 12 months ago, however, when suffering a tough-to-take aggregate defeat to rivals Liverpool, and their stuttered run of form over the past fortnight certainly does not make this a formality.
Recent European form: LWWWWD
Recent form (all competitions): WWWDDL
United welcome Rostov as strong favourites to make it through, even if Mourinho insists that a "difficult match" awaits against a side just inside the top half of the Russian top flight, citing the visitors' experience of playing in "big matches".
Rostov have previously held PSV Eindhoven to successive draws and defeated Bayern Munich in this season's Champions League, while also convincingly seeing off Ajax in the preliminary round, but most of their success has come on home soil.
The build-up to last week's first-leg tie in Russia was dominated by the state of the Olimp-2 playing surface, which even had Mourinho calling on UEFA to consider calling off the match, or potentially moving it to another venue, as he feared one of his players picking up an injury.
As it turned out United navigated the surface well enough, taking the lead through Henrikh Mkhitaryan's strike - the third game in a row he has found the net in the Europa League, leaving him behind only Ruud van Nistelrooy in that regard (nine in a row in 2002-03) - before being pegged back before the hour.
If nothing else, though, those aforementioned results for Rostov - as well as the recent 5-1 aggregate thrashing of Sparta Prague in the previous round - shows that they cannot be completely written off, even if they do not have the leveller that is their Olimp-2 home pitch.
Managed by former Moldova boss Ivan Daniliants, Rostov find themselves in good form thanks to a five-match unbeaten run since returning from Russia's three-month winter break, while going further back it is just one defeat in 14 overall for last season's domestic runners-up.
The Selmashi were unable to follow up their thumping of bottom club Tom Tomsk with victory against Terek Grozny at the weekend, being held to a stalemate by the side directly above to see them remain in eighth place and four points off a top-four finish.
While a first-leg draw may have suited the Red Devils more so than their opponents, thanks to the bonus of an away goal, the omens are not so good for the English giants when it comes to drawing the opening 90 minutes of a two-legged tie.
United may have progressed in five of their last seven European knockout ties when that has been the case, but on both of the last occasions - Real Madrid in 2013, Bayern Munich 2014 - they have crashed out in the second leg, providing another warning sign that the job is far from done just yet.
Picking up an aggregate victory at Old Trafford really would take something special as far as Rostov are concerned, however, as the 2014 Russian Cup remains their only previous major honour, with this their second-ever European knockout stage away fixture.
Recent European form: LWDWDD
Recent form (all competitions): WWDWDD
United will be glad to call upon the services of top scorer Zlatan Ibrahimovic once again on Thursday, with his three-match ban only applying to domestic games, while Ander Herrera - controversially dismissed at Stamford Bridge - will also be involved.
There is also a place in the squad for centre-back Eric Bailly, who missed the first leg through a suspension of his own but is now free to return in the heart of defence, likely alongside Marcos Rojo as he is facing a five-match domestic exclusion if found guilty of stamping on Eden Hazard.
Discipline is proving to be an issue for the Red Devils, then, but they certainly have a strong squad and may even have illness victims Wayne Rooney and Anthony Martial back among their ranks in time for this evenly-poised match.
First-choice goalkeeper Soslan Dzhanayev is expected to return between the sticks after overcoming injury, but Nikita Medvedev is standing by should the second leg come too soon for the Russia international.
Manchester United possible starting lineup:
De Gea; Valencia, Rojo, Bailly, Blind; Herrera, Pogba; Mata, Mkhitaryan, Martial; Ibrahimovic
Rostov possible starting lineup:
Dzhanayev; Mevlja, Navas, Kudryashov; Terentjev, Erokhin, Prepelita, Noboa, Bayramyan; Bukharov, Poloz
Head To Head
Man United have never previously lost to a Russian side on home soil in European competition, although three of those previous four encounters have ended all square.
Rostov will make their first trip to England for this tie, a week on from their first meeting against the Red Devils, knowing that Russian teams have won on just two of their last 26 visits to English soil.
Since the start of 2015-16, Russian clubs have faced off against English opposition seven times in competitive action and have not won any of those matches, losing four and drawing the other three.
We say: Manchester United 2-0 Rostov (United through 3-1 on aggregate)
Rostov may not be heavyweights on the continent, having only made their first appearance in European competition the year after Man United prevailed at Camp Nou to complete a famous treble in 1999, but they have lost just three of their last 15 games on the big stage and are in a positive run of form. The hosts, on the other hand, have exited the FA Cup and lost further ground in the Premier League over the past fortnight, so they will simply be happy to get the job done by any means necessary to return back to winning ways.