The Spaniard broke the deadlock in the 14th minute with a placed finish from 20 yards before Alvarez tapped home after a neat move on the hour to seal the points.
Our dominance was perhaps best illustrated by the whopping 938 passes completed - the second most ever recorded in the Premier League only behind our total of 942 against Swansea City in 2018.
After draws in each of our last three Premier League home games, it’s a welcome three points for Pep Guardiola’s side.
Having lifted the Big Five trophies in 2023, this win leaves us two points off Premier League leaders Liverpool at the halfway point of the 2023/24 season.
The afternoon began with a celebration and then a moment of reflection.
First came a presentation of all five of City’s trophies to the Etihad crowd as well as huge banners marking the achievement.
That was followed by a period of silence for those who have a connection with either club who have died in 2023.
Once the game began, City had all the early running.
Julian Alvarez came close to opening the deadlock just two minutes in with a sweet left-footed volley that whistled past Wes Foderingham’s far post.
The deadlock was instead broken just over 10 minutes later when Rodrigo picked up the ball in midfield, skipped past one tackle, drove at the defence and slid a shot along the floor and into the far corner of the goal.
It was the midfielder’s second goal against Sheffield United this season, after smashing the late winner at Bramall Lane back in August.
With the Etihad chanting in recognition of the Champions of the World, Bernardo Silva thought he had doubled our lead in the 21st minute.
However, his deft effort was tipped wide by the advancing Foderingham.
If the Portuguese’s effort was delicate, Kyle Walker’s shot a few moments later was of the opposite nature.
He powerfully struck at goal from 25 yards but didn’t quite put enough bend on it for it to nestle inside the post.
While we passed and probed for the remainder of the half without success, the match became increasingly untidy.
That created the conditions for Sheffield United to attack as half-time drew closer.
First Phil Foden burst through and attempted to take the ball around Foderingham before Bobb’s run into the box ended with an opportunity for Alvarez that the Argentinian couldn’t keep down.
Foden, operating behind central striker Alvarez, gradually found more room as the game wore on and his quick feet looked to have formed another chance in the 56th minute until a last ditch defensive block sent his shot wide.
The second eventually came just after the hour mark thanks to the lively pair of Bobb and Foden.
Bobb, wide of the box on the left wing, threaded a ball through the eye of a needle to Foden, who took one touch and did similar to find Alvarez sliding in at the back post.
That finish marks the 23-year-old’s 15th goal in 50 Premier League appearances.
20-year-old Bobb could have had his own a few minutes later when he picked up the ball 10 yards out, but defender George Baldock matched his quick footwork and shot.
Alvarez, tireless as always, came within inches of a second when he closed down a Foderingham clearance.
However, the striker could only watch as it ricocheted off his shin and flew beyond the frame of the goal.
City focused on retaining possession in the closing stages, eventually racking up a whopping 938 passes.
It sealed a third calendar year without a home defeat, having also done so in 2011 and 2017.
Subs: Ortega Moreno, Phillips, De Bruyne, Gomez, Nunes, Hamilton
SHEFFIELD UNITED XI: Foderingham, Bogle, Baldock, Trusty, Robinson (C), Thomas (Norrington-Davies 90), Norwood, Souza, Ben Slimane (Brewster 67), Brooks (Osborn 80), Osula (Archer 67)
Subs: Davies, McBurnie, Traore, Larouci, Seriki
Man of the match
Rodrigo - The midfield metronome continues to shine.
His influence on this team throughout 2023 has been way beyond that of a defensive midfielder.
In fact, the Spaniard is almost unrecognisable from the player that first arrived at City in 2019.
His work with Pep Guardiola has seen him develop into a special player in almost every area of the game.
That’s even before you consider the key strikes in games such as June’s UEFA Champions League final.
Today’s turn saw him score our first and act as the team’s driving force throughout the 90 minutes.
Pep Guardiola reaction
“First half was a little flat, everything was flat.
“At half-time for the first time I didn’t talk one word about tactics, I took a chair and said guys when you go out with a smile on your face and enjoy we are going to win.
“In the second half, the first 15/20 minutes was the best minutes we had and that helped us win the game.
“Second half we lift, especially with Oscar [Bobb]. He helped us to increase our rhythm and movements to the byline.
“He’s really good in small spaces like Phil, Bernardo, Rico. Against teams like Sheff Utd we have two options but for crosses Erling is not there and Gundo is not there anymore.
“So we attacked in the pockets and made a good game.”
The Big Five
2023 has been a year like no other for Manchester City.
In our first home match since being crowned Champions of the World and sealing our fifth major title of the year, there was plenty of cause for celebration at the Etihad.
Firstly, all five pieces of silverware were in suspension above the Blue Carpet that welcomes our players off the team coach every game.
Then, ahead of the teams coming out of the tunnel for kick-off, the trophies were carried pitchside by five loyal fans.
At the same time a giant tifo was unfurled over the East Stand with the trophies on.
Meanwhile, the now famous ‘best team in the land and all the world’ message taken from the long-adored chant initially sung at Maine Road covered the centre circle.
2023 at the Etihad Stadium
As Champions of England, Europe and the World, we know these are great times to be a City fan.
However, it’s always worth repeating just how brilliant it currently is to see this side in action at the Etihad Stadium.
In 28 games at our home in 2023, we have won 25 and drawn three. During that time we’ve netted an incredible 87 goals and conceded only 19.
As much as the numbers demonstrate the level of this team, it’s the nights against the likes of Arsenal, Bayern Munich, Real Madrid that will live forever in the memory.
What it means
City hit the halfway mark of the Premier League campaign with 40 points from 19 matches.
This victory sees us pile the pressure on league leaders Liverpool, moving just two points behind Jurgen Klopp’s team having played the same amount of games.
City have the rare luxury of a full week to prepare for our next game, with Huddersfield Town the visitors in the third round of the FA Cup at 14:00 on Sunday 7 January.
Our next Premier League assignment sees us travel to Newcastle United for a 17:30 start on Saturday 13 January.
News about Man City v Sheff Utd
City 2-0 Sheffield United: Tunnel Cam
Go behind-the-scenes as City closed our phenomenal 2023 with a 2-0 Premier League win over Sheffield United at the Etihad. Watch more
Guardiola: De Bruyne return is ‘incredible news’
Pep Guardiola was delighted to name Kevin De Bruyne on the bench this weekend as the midfield playmaker enters ‘the last stages, the last steps’ before playing for City again. Read more
Guardiola hails Bobb impact in 2023 finale
Pep Guardiola praised the impact of Oscar Bobb in the 2-0 victory over Sheffield United – our final game of 2023. Watch more
City 2-0 Sheffield United: Pitcam highlights
Watch our final win of 2023 from a unique perspective on CITY+. Watch more
De Bruyne will be touched by incredible reception - Warnock
Football legend Neil Warnock says he was stunned by the reception that Kevin De Bruyne received during City’s 2-0 victory over Sheffield United. Read more
Foden has been 'outstanding', says Pep
Pep Guardiola hailed Phil Foden as ‘outstanding’ as we finished 2023 with four successive victories. Watch more
Guardiola reveals unique half-time team-talk
Pep Guardiola says three successive home draws in the Premier League caused a degree of hesitancy in his players against Sheffield United. Read more
City 2-0 Sheffield United: Extended highlights
Watch all the key moments from City's Premier League clash with Sheffield United at the Etihad Stadium. Watch more
City 2-0 Sheffield United: Brief highlights
Watch the best of the action from City's 2-0 victory over Sheffield United at the Etihad Stadium. Watch more
Full-match replay: City v Sheffield United
Watch the full 90 minutes of City’s final game of a memorable 2023 as we faced Sheffield United. Watch more