James Maddison scored twice while Pedro Porro also netted and Brennan Johnson added a fourth for Spurs deep in added time as the Londoners subjected City to their most lopsided loss at the Etihad Stadium.
The limp display left hundreds of shell-shocked City fans beating a hasty exit, ending the champion's record run of 52 consecutive home matches unbeaten in all competitions.
City manager Pep Guardiola, who signed a two-year contract extension two days earlier, has now lost five consecutive games across all competitions for the first time in his career, and three in a row in the league in his tenure with City.
The loss left City five points adrift of league leaders Liverpool, with the Reds having a game in hand. Spurs climbed to sixth.
"In this moment we are fragile defensively," Guardiola said. "In eight years we have never lived this kind of situation. Now we have to live it and break it by winning the next games, especially the next one. Now we see things in one way, maybe in a few weeks we see it differently."
LIVERPOOL EXTEND LEAD
Premier League leaders Liverpool beat bottom side Southampton 3-2 on Sunday to build a sizeable eight-point lead over reigning champions Manchester City after Mohamed Salah led a second-half comeback for the visitors.
Liverpool were trailing 2-1 when Salah scored twice in the second half to take his season's tally to 10 goals in the league, two behind the league's top scorer Erling Haaland of City.
Liverpool took full advantage City's continued poor form and Arne Slot's side now have 31 points from 12 games to City's 23 ahead of their clash at Anfield next weekend.
"They were very important, especially after being down 2-1. It's the most important thing to have won the game," Salah told Sky Sports.
"Each game is different. They had a game plan and played very well. We managed to come back and win the game. I think we have a good game plan, we played our game and I was confident we would create chances.
"Man City is Man City. They have a bad time now but they have great players... We have a game against them so hopefully, we win it and go 11 points clear."
Southampton shot themselves in the foot when they tried playing out from the back and under Liverpool pressure, Flynn Downes's pass fell to Dominik Szoboszlai at the edge of the box and the unmarked midfielder fired home to make it 1-0.
However, Southampton received a lifeline minutes later when Andy Robertson tripped Tyler Dibling on the edge of the box and the referee pointed to the spot, with VAR upholding the decision even though the contact was made just outside the area.
Although Adam Armstrong had his spot kick saved by Caoimhin Kelleher, the forward pounced on the rebound to equalise with his third goal in four games for Southampton.
That spurred Liverpool into action and after Darwin Nunez failed to find Luis Diaz at the far post for a simple tap-in, Salah took matters into his own hands.
Liverpool equalised through Salah when he ran through on goal on to a lob from Ryan Gravenberch and as he saw Alex McCarthy come off his line, the Egyptian winger took one touch to let the ball roll past the onrushing goalkeeper.
It marked the eighth time Southampton had committed an error leading to an opposition goal -- more than any other Premier League team this season -- as the home side squandered their advantage.
Southampton then conceded a penalty in the 83rd minute from a Yukinari Sugawara handball and Salah made no mistake from the spot as Liverpool sealed the three points.
"We're really disappointed with the result. They're really poor goals to give away. We've come up short again and it's hard to take," Southampton's Jack Stephens said with the club still bottom and five points from the safety zone.
"It's frustrating to concede goals but a lot of our good play came from the situations as well. We'll have to look at it back and evaluate everything, it's about getting the balance a bit better."
ARSENAL FIND FORM
Goals by Bukayo Saka, Thomas Partey and teenager Ethan Nwaneri got Arsenal back on track after four league games without a win in manager Mikel Arteta's 250th game in charge.
Arsenal stayed in fourth spot, level on 22 points with third-placed Chelsea who began the day's action with a 2-1 victory away at Leicester City, and one point behind City.
Leaders Liverpool have 28 points ahead of their Sunday clash with bottom club Southampton.
Arsenal began the day level on points with surprise package Forest but outclassed the Midlands club in the London rain.
The returning Saka and captain Martin Odegaard were hugely influential for Arsenal, combining after 15 minutes for Saka to clip a superb left-footed drive high past Forest keeper Matz Sels.
Partey curled in Arsenal's second after 52 minutes and 17-year-old Nwaneri, on as a substitute, put the icing on the cake with his first Premier League goal late on.
"It's not a coincidence. The team flows in a different way when (Odegaard) is playing," Arteta said of his skipper who returned from a long injury lay-off earlier this month.
"When he is on the team you sense something different even if it's hard to put your finger on it."
NEW MANAGER, SAME UTD
Goals by Nicolas Jackson and Enzo Fernandez secured the points for Chelsea as their manager Enzo Maresca returned to haunt his former club. Jordan Ayew's stoppage-time penalty came too late for the hosts.
Aston Villa have now gone six games without a win in all competitions as their early-season surge has stalled.
They needed a late headed equaliser by Ross Barkley to take a point against a Palace side who twice led.
Ismaila Sarr gave Palace the early lead before Ollie Watkins levelled and the hosts then squandered a chance to go ahead as Youri Tielemans had his penalty saved by Dean Henderson. Justin Devenny restored Palace's lead almost immediately but the Londoners were unable to secure only their second league win.
Matheus Cunha scored two superb goals to take his league tally for the season to seven and also set up a third for his side after Fulham went ahead after 20 minutes with an Alex Iwobi curler from the edge of the box.
Wolves' second league win of the season put them on nine points from 12 games and into 17th place.
Brighton & Hove Albion joined Arsenal and Chelsea on 22 points with a 2-1 victory at Bournemouth thanks to goals by Joao Pedro and Kaoru Mitoma as they maintained their best-ever start to a top-flight season.
The visitors did end with 10 men though after Carlos Baleba was shown a second yellow card on the hour.
Everton had 27 goal attempts at home to 10-man Brentford but could make none of them count as they drew 0-0 -- a result that left them in 15th place in the table. Brentford played half the game with 10 men after Christian Norgaard was dismissed for a bad challenge on Everton keeper Jordan Pickford.
