It was the perfect response to Friday’s setback at Wolves and also marked the 100th Premier League win of Pep Guardiola's City reign.
The visitors had a first half effort disallowed by VAR and proved more than a handful for the champions.
There was also a touch of controversy about Aguero’s 52nd minute opener, with the Blades claiming referee Chris Kavanagh had impended a player in the build-up, but De Bruyne’s late strike sealed the deal and ensured that we ended an unforgettable decade with a vital three points.
Unbeaten away in the league all season so far, the visitors illustrated their confidence and prowess by making the more assured start.
Compact and tight at the back with two solid banks of four, combined with a lively, pacey threat upfront, Chris Wilder’s team almost broke the deadlock on eight minutes, the dangerous Lys Mousset finding a yard of space in the box before narrowly heading Callum Robinson’s inviting cross wide under pressure from Oleks Zinchenko.
A sublime Rodri through ball to Mahrez got City motoring on 17 minutes, only for the Algerian’s shot from the right channel to be parried wide by visiting keeper Dean Henderson.
United through remained a potent attacking threat with John Egan seeing a 25th minute header power just over the bar.
And the visitors thought they had made the breakthrough on 28 minutes when, from a stunning curling delivery from John Fleck, Mousset sprinted through before firing past Claudio Bravo, in for the suspended Ederson.
Once again, however, VAR had the final word, a subsequent check demonstrating that the striker was fractionally offside.
Mousset’s electric pace saw him evade the City’s high press back line once again but, with only Bravo to beat, he fortunately chose the wrong option, shooting into the side netting.
It was a frustrating first 45 minutes for Guardiola’s side, encapsulated by Zinchenko’s speculative shot from outside the box which sailed harmlessly high.
Mousset’s pace again caused problems straight after the restart, the striker finding Muhammed Besic whose 18 yad effort struck the stanchion.
It needed some inspiration on our behalf and, not for the first time, it arrived via Sergio Aguero.
Our all-time record scorer needed no second invitation, unleashing a powerful blast for his first goal since early November.
The visitors were angry claiming that referee Kavanagh had played a decisive role in touching the ball to KDB and blocking Fleck but, after another VAR check, the goal stood.
The contest was still alive though and Bravo needed to be alert to twice punch clear as the visitors looked to respond.
City had a reasonable shout for a penalty after a Mahrez shot appeared to strike the arm of a Blades defender but Kavanagh was unmoved.
And the game was then put to bed on 81 minutes in emphatic style by De Bruyne.
19 - Kevin De Bruyne has been directly involved in 19 goals in the Premier League this season (seven goals and 12 assists) - only Jamie Vardy has had a hand in more (20). Freakish. #MCISHU pic.twitter.com/6ltW29igWw— OptaJoe (@OptaJoe) December 29, 2019
Mahrez was the architect, sweeping a pass through to the Belgian who cut inside before drilling home an emphatic finish in the bottom left hand corner.
Billy Sharp almost narrowed the deficit with an injury time header which struck the post and rolled across the line, but for a City side playing our second game in 46 hours, it was a priceless three point haul.
And it marked 100 league wins in England for our manager, a feat he has achieved in record time.
⚽️ @aguerosergiokun's goal today was his 174th in PL, the top scorer in the competition in the 2010s.— Sky Sports Statto (@SkySportsStatto) December 29, 2019
PL top scorers in the last decade:
174 Sergio Aguero
136 Harry Kane
114 Wayne Rooney
113 Romelu Lukaku
98 Robin Van Persie
97 Jamie Vardy pic.twitter.com/wKASq6Sq5Z
The Blades also became the 32nd different opponent Kun has scored against in the Premier League.
Out of the 33 he has faced, only against Bolton has he failed to find the target in league action.
Man of the match
Kevin De Bruyne was a bundle of energy from start to finish and capped another superb individual display with his late goal.
He continues to go from strength to strength.
"I understand why Sheffield United are in the position they are in the table and only lost one game away so far - they have incredible physicality.
"In the first half we had problems but in the second we were much much better."
Pep on reaching 100 league wins: "It's a big compliment for the club, players and staff to achieve 100 victories.
"It's an incredible achievement for this incredible organisation and big compliments to all the players and staff we had during this period."
What it means
City remain in third place in the table but are now only a point behind second-placed Leicester, with both having played 20 games. Leaders Liverpool are 14 clear of us after their 1-0 win over Wolves.
City’s hectic festive fixture schedule continues on New Year’s Day when we play host to Everton.
Kick off at the Etihad for our first game of 2020 is 5.30pm.