Defending champions City put in a dominant performance at Old Trafford in the 191st Manchester derby on Sunday (Monday AEDT) to add to the growing pressure on United manager Erik ten Hag.
It was United's seventh loss of the season in all competitions and leaves them 11 points adrift of Ange Postecoglou's leaders Tottenham in the league.
City's win moved them to within two points of Spurs at the top and they looked ominously good, with Haaland scoring a first-half penalty and then doubling the visitors' lead with a header shortly after halftime.
He then provided the cross for Phil Foden to complete the scoring and prompt United fans to leave the stadium early.
Haaland has now scored 13 goals in all competitions this season and might have had more if not for the efforts of United goalkeeper Andre Onana, who produced a number of fine saves to keep City at bay.
Before kick-off, both teams had come together to commemorate United great Bobby Charlton, who died earlier this month. Past players from both sides of the city entered the field to join in a moment of applause.
Diogo Jota shows support for the plight of teammate Luis Diaz in Liverpool's Premier League win.
In one stand United fans were invited to raise white paper that read out "Sir Bobby" in giant lettering. Elsewhere a huge banner was unfurled with a picture of him lifting the European Cup trophy in 1968.
Earlier, Liverpool had shown their support for the plight of striker Luis Diaz during a comfortable 3-0 win over Nottingham Forest in the Premier League.
Quickfire goals from Diogo Jota and Darwin Nunez before the break and Mohamed Salah's second-half effort helped Jurgen Klopp's side maintain their 100 per cent league home record this season.
Jota ran to grab Diaz's number seven shirt from Klopp after scoring, with the Colombian not featuring in Liverpool's squad following reports his parents had been kidnapped in his homeland.
Liverpool's latest victory - their eighth in a row in all competitions at Anfield - was their seventh from 10 league games in this campaign and lifted them back to within three points of Spurs in fourth place.
At West Ham, Dominic Calvert-Lewin's landmark second-half strike secured a 1-0 win for Everton.
The striker scored six minutes after halftime at the London Stadium on Sunday (Monday AEDT) as Everton won for only the third time in the league this season.
For Calvert-Lewin, who has had to contend with a slew of injuries, it was his 50th league goal for the club as he joined Romelu Lukaku, Duncan Ferguson and Tim Cahill in reaching the half-century mark.
Aston Villa maintained their strong start to the season with a dominating 3-1 victory over newcomers Luton, their fifth win in six league games.
John McGinn, Moussa Diaby and an own goal from Luton captain Tom Lockyer made it a comfortable afternoon's work for Villa, before a consolation comedy 83rd minute own goal, when defender Ezri Konsa's header bounced back off the bar and in off goalkeeper Emi Martinez.
In the day's other game, Fulham escaped with a 1-1 draw at Brighton, who dominated the first half to go in one-up through an Evan Ferguson goal but were then pegged back by a stunning Joao Palhinha equaliser in the 65th minute.
With agencies
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