There was further good news with Kevin De Bruyne at his sublime best in midfield as he claimed yet another assist in his first start since August following surgery.
There were some welcome faces returning on and off the pitch with De Bruyne and Stones returning to the City line-up as two of six changes from the side that beat Tottenham, along with Haaland returning to the bench.
Former captain Vincent Kompany also returned, in the Burnley dugout, and received the warm reception from the Etihad fans that his legendary status deserves as well as huge hug from Pep Guardiola, but all friendships were put on hold once the match kicked off.
The Burnley boss was prepared to play the passing football that proved successful in clinching promotion last season but they were almost undone by a free-kick inside five minutes.
Nunes was proving a big threat running through the middle and it was another of his breaks that led to the opener.
The Portuguese international raced onto Phil Foden’s incisive pass and when his low cutback was blocked by Dara O’Shea, he steadied himself to pick out Alvarez with a perfect cross for the birthday boy to head home.
He then doubled City’s lead six minutes later with a cleverly worked free-kick.
Around 30 yards from goal, De Bruyne slid a clever pass down the side of the Clarets wall for Alvarez to finish coolly with a clipped finish.
Former Academy keeper James Trafford was another familiar face and he made a big save deny Nunes his first goal for City with a fierce dive from a tight angle while Josko Gvardiol’s effort from a similar position curled just wide of the far post.
Burnley made it through to half-time without conceding again but were undone inside 25 seconds after the restart.
De Bruyne played a ball inside the full back to release a flying Foden who sprinted clear before squaring to Rodrigo and the Spaniard curled in a delicious third from the edge of the box with a finish reminiscent of his Champions League final winner.
Lyle Foster went close for the visitors with a shot over the bar but it was a rare break from the dominant display from the Blues as we enjoyed more than three quarters of the possession.
Job done, De Bruyne was given a well-earned rest after 70 minutes and left to his name once again ringing around the Etihad.
While the Clarets may have been glad to see the back of him, it led to the introduction of the imposing figure of Haaland.
Seconds after coming on, he made a strong but fair challenge that left O’Shea in discomfort, although it was Rico Lewis who started the real argy-bargy.
Haaland did get a couple of sights of goals. His first saw him driven wide before taking a wild airshot which left him smiling, along with his teammates on the bench, and a far-post header was smuggled out for a corner.
But it was Burnley that scrambled a late goal with Ameen Al-Dakhil turning in David Datro Fofana’s cross to spoil Ederson‘s clean sheet.
Subs not used: Ortega-Moreno, Walker, Dias, Bernardo, Bobb
BURNLEY: Trafford, Vitinho, O’Shea, Ekdal (Massengo 86), Al-Dakhil, Gudmundsson (Ramsey 59), Berge, Brownhill, Odobert (Zaroury 76), Foster (Fofana 59), Amdouni (Roberts 59).
Subs not used: Muric, Cork, Cullen, Bruun Larsen
Man of the match: ALvarez
The Argentinian signed for City on his 22nd birthday and it was another day to remember on his 24th.
Alvarez led the line although it was a fluid display from the team, with players taking up plenty of dangerous positions.
But he showed his striker’s instinct by finding space in a crowded box to head home Nunes’ cross for the opener.
And his second was a well-timed run and exquisite finish that all-but killed off the hopes of the visitors.
Set-piece coach Carlos Vicens earned a high-five from Guardiola after a free-kick routine led to City’s second in the 22nd minute.
Of course, you still the need the quality of De Bruyne and Alvarez to make it work and the Belgian produced a perfectly weighted pass which the striker finished neatly.
But it was a move developed on the training ground by Vicens and analyst Jack Wilson and comes four days after the 1-0 win at Tottenham when City repeatedly fired over corners just under the crossbar to test keeper Guglielmo Vicario and it finally led to Nathan Ake’s late winner.
With stubborn defences focused on stopping the City threat, it can be the little details that prove decisive and while our qualities have been built on passing football, nothing is overlooked to try to gain an edge.
“Today the game was not close. There are games with this score that feel closer, this was not. We had players who have less control than usual, we had more runners, more speed.
“Burnley is not an easy team to face, they never give up. Today, we won because of the quality of players we have, not because we controlled everything or where better at all aspects.
“I have the feeling Burnley did not get the result they deserved to take. Vinny sooner or later will finish here. I have the feeling that he will finish here. He is already a big manager, what he did last season with Burnley.
“You can see the ideas they have, the way they try to defend. I like what he does.”
DE BRUYNE REACTION
“It feels great obviously. The last time I started was against Burnley at the start of the season about six months ago.
“Now I’m feeling good. Progressing now and I’m happy. I’m going in the right direction.
“Yesterday, we worked a bit on [the free-kick].
“At the beginning I didn’t really want to do it. But the defender with Julian moved into the middle a bit. So he opened the space for Julian to go into.
“I just had to put it straight with the right speed and Julian did the rest. We practised it for Burnley, but it can work against other teams.
“I think, like you see Pep was lively with his staff, because if you pull it off they’re happy. They give you the options, front post, second post, trick plays, and a little bit of seeing what is possible. When you pull it off, it’s a nice goal.”
WHAT IT MEANS
City move back up to second in the Premier League, moving above Arsenal who won on Tuesday night.
Liverpool remain five points clear after beating Chelsea 4-1, but City have a game in hand on the leaders and still have to travel to Anfield.
We’re back in Premier League action on Monday, 5 February when we face Brentford.
It will be our first game against the Bees this season as we travel to the Gtech Stadium for the 20:00 (UK) kick-off.
Our next home at the Etihad is on Saturday, 10 February when Sean Dyche’s Everton are the visitors.
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