The Norwegian's double maintained City's 100 per cent start to the league after Yoane Wissa had fired Brentford ahead with just 22 seconds on the clock.
But Liverpool lost for the first time under their new manager Arne Slot, shocked at their Anfield home by a smash-and-grab 1-0 raid by Nottingham Forest.
Elsewhere in the English top-flight on Saturday, Manchester United won at Southampton 3-0 to bring some relief for manager Erik ten Hag after their poor start to the season and Chelsea rode their luck before substitute Christopher Nkunku's goal in the 86th minute sealed a 1-0 win at Bournemouth.
At the Etihad, Haaland scored his 98th and 99th goals in his 103rd City appearance in all competitions, and was the width of the post away from his third consecutive hat-trick after trebles against Ipswich Town and West Ham United.
"He's been really, really good. I would say he's the best he's been, but it's only four fixtures this season," City manager Pep Guardiola said.
Erling Haaland slots home his side's second goal in the victory against Brentford. (AP PHOTO)
Haaland, who has been nominated for the Ballon d'Or, now has nine goals in four league games.
His first after 19 minutes levelled the scores and he was then too strong for defender Ethan Pinnock, shaking off the Brentford man and running through for his second in the 32nd.
He was inches away in the 81st minute; his shot coming back off the post after he beat the keeper.
Liverpool boss Slot suffered his first setback in English soccer after Callum Hudson-Odoi fired Forest to a stunning win on Merseyside.
Hudson-Odoi struck in the 72nd with a brilliant curling effort from the edge of the box and beyond goalkeeper Alisson.
Liverpool had been the only team other than City with a perfect record after the first three matches.
"Far too many times we lost the ball around the area, it was not good enough," Slot said.Â
"We have to be better with the ball. Our decisions and execution wasn't good enough."
Marcus Rashford snapped a 12-game barren run in front of goal for Man United, doubling their lead at St Mary's after Matthijs de Ligt had scored his first for the club. Substitute Alejandro Garnacho netted a third in the sixth minute of added time.
Marcus Rashford punches the air after ending his goalscoring drought at Southampton. (AP PHOTO)
The win came after back-to-back defeats and was a tonic for Rashford, who hadn't scored since March in United's FA Cup quarter-final win over Liverpool.
It could have been a different story, though, if Cameron Archer had converted a Saints penalty in the 33rd. Instead, his effort was saved by goalkeeper Andre Onana.
Newly promoted Southampton were reduced to 10 men when Jack Stephens was sent off in the 79th for a high challenge on Garnacho.
Aston Villa produced a terrific comeback to beat Everton 3-2, goals from the Toffees' Dwight McNeil and Dominic Calvert-Lewin being answered by a brace from Ollie Watkins and a 76th-minute winner from Jhon Duran.
Everton remain bottom, the only team without a point.
There was late drama as Jean-Philippe Mateta converted an added-time penalty to salvage a 2-2 draw for Crystal Palace against Leicester City.
Leicester led 2-0 at Selhurst Park after goals from Jamie Vardy and Stephy Mavididi, but Mateta sparked Palace's response with a goal in the 47th, a minute after Mavididi doubled the Foxes' advantage.
West Ham left it even later to salvage a point in a 1-1 draw at Fulham, with Danny Ings striking in the 95th minute, while Brighton & Hove Albion were frustrated by a goalless draw at home with Ipswich.
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