For the first time since taking over from Jose Mourinho, interim boss Ole Gunnar Solskjaer was feeling the heat.
His side were thoroughly outclassed midweek by Paris Saint-Germain to leave them with an uphill struggle to make the Champions League last eight, raising doubts over whether the Norwegian was the right man for the job having tasted defeat for the first time on the bench.
On the pitch, meanwhile, Paul Pogba had his own critics to silence.
Transformed since the dark days of Mourinho, the Frenchman nonetheless suffered a regression on Tuesday with an unnecessary late foul on Dani Alves that earned him a second yellow card that rules him out of the return fixture at the Parc des Princes.
Pogba has been a revelation under Solskjaer but, like his manager, the midfielder needed to show he could deliver when it most counted. He did all that and more in a 2-0 win at Stamford Bridge that sent United marching into the next round and piled further pressure on the beleaguered Chelsea supremo Maurizio Sarri.
Unwilling or, perhaps, unable to meet Chelsea's exhausting high-octane approach head on after struggling to keep up in a hectic opening to proceedings, Solskjaer decided that less was more in west London.
Sarri's men were granted the lion's share of possession and invited to hurt the visitors in any way they could, a risky strategy that threatened to backfire early on when Gonzalo Higuain was gifted a free header in the area.
Happily for the visitors, the Argentine steered his effort wide of compatriot Sergio Romero's left-hand post and United earned a reprieve for their somewhat slapdash marking. That near-miss prompted a general tightening across the back and, while Eden Hazard's quick feet were a constant thorn in the Reds' side, the Belgian's slippery dribbling did not translate in further danger for Romero.
It was at the zenith of Chelsea's dominance that United found the breakthrough courtesy of Pogba.
Breaking on the left off a pass from the equally excellent Juan Mata, he waited just long enough for Ander Herrera to break into the box on the shoulder of Marcos Alonso, apparently too preoccupied with chasing butterflies under the floodlights in the west London evening to notice his countryman moving for goal. Pogba's cross was executed perfectly and Herrera barely had to break stride to nod past Kepa and open the scoring.
A matter of minutes later, it became all too clear that the Blues had failed to learn their lesson.
Once more a passage of broken play in the middle of the field led to a United player, this time Marcus Rashford and this time on the right wing, breaking clear with no marker in sight. And once again no Chelsea defender had the presence of mind to pick up the midfielder decked in red who had ghosted through their porous backline to meet an inviting cross with a thumping header.
Chelsea huffed, puffed and took even more of the ball in the second half but they found no way past a formidable United defence, failing to register a single shot on target after the break.
Having made the difference in the Chelsea area earlier, Herrera and Pogba tucked alongside Nemanja Matic after the break to form an unbeatable barrier, capping a terrific all-round performance from Solskjaer's men as a whole and the Frenchman in particular.
Now averaging a goal or assist every 68 minutes under Solskjaer, Pogba has been absolutely vital to United's post-Mourinho renaissance and he proved decisive again to book the club's passage to the FA Cup quarters.
Equal credit, however, belongs to the rookie Norwegian, who has ridden out this first crisis – at Old Trafford, after all, one is never more than 90 minutes away from perceived meltdown – to prove that talk of his being out of his depth is at the very least premature.
Solskjaer is equally an easy target for critics: a relative novice on the bench in one of the world's most demanding jobs. Thus, any weaknesses will logically see demands for a more experienced head to take over at the end of the season.
He has plenty of admirers, though.
“He has got them into the top four – something no-one thought was possible this season – but they lose one game to a team full of superstars and people start talking sh*t again,” former United star Dimitar Berbatov fired in typically colourful terms to Betfair in the aftermath of Champions League disappointment and as the usual vultures began to circle.
“It's the way of the world these days but everyone who understands football knows what a good job Ole has done.”
Ryan Giggs and Paul Scholes have voiced similar opinions: forget Mauricio Pochettino or any other potential suitor, Ole is the man for the job.
The Champions League trophy may be a step too far for Solskjaer and Pogba this season. But Monday's masterclass keeps the FA Cup on the horizon, and if the Reds can keep up their form in the Premier League, a place in Europe's premier tournament – a near-impossibility a matter of weeks ago – is well within reach.
A slip is not a fall, the old adage goes – and the two masterminds behind United's recent revival have dusted themselves off and shown that they remain on the right track.