The victory also saw City set another new Premier League record as it was our 21st consecutive win at the Etihad – beating the previous best run of 20 set by Manchester United.
Alvarez and Haaland had fired City into a 2-0 lead at the break before Brighton narrowed the deficit after the break through substitute Ansu Fati to set up a nervy last 15 minutes made all the more twitchy when Manuel Akanji was sent off deep into nine minutes of injury time after picking up a second yellow card.
But City held firm to provide the perfect response after successive league setbacks against Wolves and Arsenal and it also marked the ideal return in the wake of the October international break.
With Arsenal drawing 2-2 at Chelsea later on Saturday it meant City retained top spot on goal difference following a performance that was full of positives for Pep Guardiola and his players.
The meeting with Roberto De Zerbi’s side brought together two of the Premier League’s most attacking and aesthetically pleasing sides.
Beforehand there was a poignant moment as a huge Tifo in tribute to the late, great Francis Lee was draped across the East Stand.
Ahead of the game, Pep Guardiola had spoken of his admiration for Seagulls boss De Zerbi and his philosophy and from the off it was clear both teams had come to play.
A fifth minute sweeping move saw Jeremy Doku fire just wide before City struck with a seventh minute opener through Alvarez.
Doku was the architect this time, powering down the left flank before arcing into the box and drawing the ball back to the waiting Argentine.
Alvarez’s left-footed strike might not have been the sweetest of his career, but it powered in via his other foot to deceive Seagulls keeper Jason Steele and nestle in the back of the net.
It was his seventh goal of the season and one that helped get City off to the perfect start.
Brighton continued to try and play but City looked in the mood – none more so than Haaland who demonstrated his hunger by rifling home a stunning strike to double our advantage on minutes.
The Norwegian received the ball midway in the Brighton half and powered forward before unleashing a thunderous 20-yard strike past Steele to rack up his 13th goal of the season and end a run of four games without a goal.
Phil Foden and Doku looked electric every time they received the ball, with Guardiola’s side continually asking searching questions of Brighton with our Belgian winger unlucky to see a 26th minute shot whistle wide after another surging run initiated by Foden.
With Rodrigo restored as the holding midfielder after his three-match ban and an imperious John Stone making his first Premier League start of the season there was both a grace and guile about City in the opening 45 minutes that made for bewitching viewing at times.
Brighton provided a reminder of their threat six minutes after the restart when Pascal Gross pinged in a close range shot that was just the wrong side of Stefan Ortega’s goal after wriggling free in the City box.
However more Foden brilliance teed up Haaland on 67 minutes as the England international’s teasing ball found our striker in the centre of the box.
On this occasion though Steele was able to parry away the City man’s shot.
Goalkeeper Stefan Ortega then came to City’s rescue after substitute Fati had spotted a gap and put in the dangerous Mitoma.
However, Ortega – making his first Premier League appearance of the season – rushed out of his box and made a fine stop to deny the Brighton man.
At the other end Dunk then prevented an Alvarez goal after Steele had dashed out of his goal to nick the ball off the advancing Doku.
Brighton were threatening though and on 74 minutes they narrowed the deficit through Ansu Fati, the on-loan forward neatly converting from close range after City had failed to clear a dangerous attack.
It made for a nervy finale - made all the more so when Manuel Akanji was sent off deep into injury time after picking up a second yellow card.
But City deservedly held firm to claim a vital three points.
Subs: Ederson, Phillips, Kovacic, Gomez, Nunes, Lewis
BRIGHTON: Steele, Julio, Dunk, Milner (Veltman 45), March (Van Hecke 92), Pedro (Fati 66), Gross, Welbeck (Ferguson 16), Baleba (Gilmour 66), Mitoma, Adingra.
Subs: Verbruggen, Webster, Dahoud, Lallana.
But Belgian winger Jeremy Doku was a veritable livewire presence all afternoon, proving a thorn in the side of Seagulls’ left back Igor Julio and creating havoc with his pace and trickery from the word go.
Doku it was who also provided the assist for Julian Alvarez’s early opener and the 21-year-old already looks right at home both at City and in the Premier League.
It was a dynamic display that only augurs well looking ahead to the rest of the campaign.
Going into the game two successive Premier League defeats had represented somewhat of a slump by City’s lofty standards – but this was an timely reminder of just what sets Guardiola’s side apart from the rest.
From passing and pressing through to technique and tenacity it was the champions and Treble winners back at our driving, aggressive best in the first half while they then showed their grit and character to dig deep when needed to after the break.
There were numerous individual and collective positives – and all against a talented and dangerous Brighton opposition.
It was the perfect response to those Wolves and Arsenal setbacks – and a welcome return to winning ways after the October international break.
City look hungry and back in the groove.
What it means
A seventh Premier League win of the season restored City to top spot in the Premier League table.
City have now accrued 21 points from nine games.
Arsenal have the same tally following their 2-2 draw at Chelsea on Saturday tea time but City boast the better goal difference so have pole position.
The pair lie a point clear of third placed Liverpool and Tottenham, who play on Monday.
All in all, this was ideal way for City to resume action ahead of a busy few weeks both domestically and in Europe.
After the two defeats it was important performance. The credit I give to Roberto (De Zerbi), they were exceptional.
I give credit to the team for victory.
In terms of Jeremy Doku, he is an exceptional winger.
He got to the byline and got us the first goal. He did many actions.
I have been really pleased for his impact since he came into us. It’s the start of many years in this house.
Jeremy doku reaction
“I’m happy with the result. After some difficult results we had in the past weeks. It’s important mentally and I hope we can keep going like this,.
“It was very important. Not only for the table but jut for us in our heads. It was a difficult game but we’re a good team, the best team for me.
“We have to prove it every time we’re on the pitch. Today we did it.”
City are back in action on Wednesday evening when we resume our Champions League group campaign away to Young Boys of Switzerland.
The reigning European champions have made a superb start to our defence of the crown having won our opening two Group G games against Red Star and RB Leipzig.
Kick-off in Berne is slated for 20.00pm (UK).
That is then followed by the small matter of the first Manchester derby of the season next Sunday when we visit Old Trafford to take on Manchester United, with kick-off set for 15.30pm (UK).
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