Nottingham Forest's English midfielder #14 Callum Hudson-Odoi (C) controls the ball during the English Premier League football match between Liverpool and Nottingham Forest at Anfield in Liverpool, north west England on September 14, 2024. AFP
Earlier, Manchester United eased the pressure on Erik ten Hag with a comfortable 3-0 win at Southampton.
Forest had not won at Anfield in the top flight for 55 years but the home faithful were stunned when Callum Hudson-Odoi fired in the winner 18 minutes from time.
Liverpool had won all three of their opening games under Slot without conceding, including a 3-0 win away at Manchester United two weeks ago.
But the Reds were sloppy and sluggish after the international break and made to pay.
Luis Diaz hit the post and Diogo Jota wasted a big chance to put Liverpool ahead before half-time.
And they were punished when Hudson-Odoi latched onto Anthony Elanga's pass, cut inside and unleashed an accurate strike low beyond Alisson Becker.
Victory lifts Forest into fourth with eight points from their opening four games.
Haaland denied hat-trick history
City took full advantage of Liverpool's defeat to move clear at the top by stretching their 100 percent record to four games despite a disastrous start.
John Stones was recalled by Pep Guardiola for his first club start of the season but the England international's poor clearance teed up Yoane Wissa to open the scoring after just 22 seconds at the Etihad.
However, Haaland's form at the start of the season remains unstoppable, even if the Norwegian just missed out on a record third consecutive hat-trick in the Premier League.
The 24-year-old's powerful deflected effort brought City level before he showed a combination of strength and skill to shrug off Ethan Pinnock and dink the ball over the onrushing Mark Flekken.
Only the post denied Haaland another hat-trick after half-time but he now has nine goals in four games this season.
Third-placed Brighton remain unbeaten but were unable to break down Ipswich in a 0-0 draw at the Amex.
Crystal Palace came from 2-0 down to salvage a 2-2 draw against Leicester thanks to Jean-Philippe Mateta's double.
West Ham also struck late through Danny Ings to snatch a 1-1 draw at Fulham.
Arsenal face Tottenham in the north London derby in the pick of Sunday's action.
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