An early blow from Bernardo Silva powered the visitors ahead before two more goals in the space of five minutes inside the first half put the result beyond doubt.
Marcus Rashford's 70th-minute strike only gives United a remote lifeline heading into the second leg, but Ole Gunnar Solskjaer certainly cannot erase the underwhelming performance by his side on the day.
City, who stunned the hosts with a massive tactical alteration in the form of a striker-less 4-4-2, perhaps, saw the best out of the wider players in Sterling and Mahrez, with the latter also continuing his purple patch to score after the half-hour mark.
In all honesty, the Cityzens could have even been four or five up, thereby standing a chance of putting the tie beyond doubt. Meanwhile, United looked short of ideas and were subsequently beaten on all fronts.
On that note, we rate the home team following their dismal display in the first leg of the Carabao Cup semi-final against Manchester City.
David de Gea - 6/10
Nowhere in the reckoning when Bernardo's sweet strike found the top corner, or when Mahrez wriggled through, but David de Gea produced a couple of match-defining moments on either half to keep his side in the contest ahead of a gruelling second leg.
He produced a great block to deny Mahrez a second, just before Rashford scored United's solitary goal of the evening.
Aaron Wan-Bissaka - 5/10
Wan-Bissaka stood firm against Sterling, and although he wasn't left reeling on his heels, the youngster was beaten by a tactical overload from Guardiola. Not to mention, his dry spells in the opposition half continue.
Phil Jones - 2/10
How on Earth could he allow Bernardo to swiftly take it down his favoured side and plant the ball into the top corner? Huge credit to the Portuguese international, but Phil Jones simply stood to watch his side fall behind. Likewise, he was simply humiliated by de Bruyne for the Andreas Pereira-own goal.
Jones looked out of place, positionally and tactically. He felt the lunges and stretches of starting a game after an age.
Victor Lindelof - 3/10
Lindelof, who has been brilliant all season otherwise, put in a shocker tonight. He was nowhere near Bernardo's through pass for City's second; a trait one wouldn't associate with the Swede given his positional awareness and intelligence in the penalty area.
Two men further forward in the form of de Bruyne and Bernardo Silva, ust proved too good for Lindelof.
Brandon Williams - 4/10
Williams showed a lot of promise venturing and galloping forward, without any significant output. He's got the willingness, but this was a different ball game orchestrated by Guardiola himself.
City looked peerless, ruthless and unforgiving. They held the courses of the fixture, ran beyond and through Williams' side many a time and gave him a torrid phase with Mahrez and the midfielders pervading his space.
Williams could even have been sent off for a nasty challenge that Mahrez opted out for, while his ill-timed challenge for City's third sparked room for improvement.
Fred - 4.5/10
Fred continued from where he had left off in recent games, but couldn't match a four or five-man midfield framework that kept it very close amongst each other and dictated proceedings at will. He was not quite there to mop up danger, or chip in with a tackle or two.
Andreas Pereira - 4/10
Credit for running his socks off throughout the evening, but that does not guarantee your side wins. Perhaps, he's not quite the playmaker Solskjaer wishes, owing to the scarcity of chances created by him ever since taking the reins down advanced positions.
Jesse Lingard - 2/10
Not up to the mark, as he squandered meaningful possession time and time again. Lingard added nothing to United's attack and stayed out of the scheme of things on the rare occasions his side spent with the ball in City's half. Subbed at halftime and rightly so.
Marcus Rashford - 6.5/10
Quite absurd to see a striker playing for Manchester United with the entire stage behind him, but remaining this isolated. Rashford saw very little of the ball in the first half, but despite the same, he sprung away to fashion a well-taken chance.
The composure he showed for the goal was praiseworthy. He's probably one man, besides Anthony Martial, who can blow caution to the wind and salvage something at the Etihad.
Daniel James - 5/10
It is no secret that Dan James has fallen prey to the arduous round of festive fixtures, with the high-intensity game such as this one testifying the same. He looked jaded, lost for pace or steam and never really got going in behind the Man City backline.
Mason Greenwood - 5.5/10
Greenwood's touches in the middle of an electric Manchester City pressing show were good to see, as he took care of the ball before playing it down and running straight through. Spurned a chance in the first half, but also took credit for the goal with a well-timed pass.
Reality check of sort, for a player who has been flying in recent weeks.
Nemanja Matic - 6/10
Surprisingly against the pace at which City were running riot, Matic brought about a sense of calm in the middle, getting close to the blue shirts and beating the press quite often.
Angel Gomes - 6/10
Certainly played a part in restoring a semblance of parity. Was lively down the channels, linking up play fruitfully and injecting new-found energy into his side's approach.
Anthony Martial - NA
Didn't quite play enough or have an instant impact.
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