Tottenham Hotspur routed Bournemouth 5-0 as they leapfrogged City into second place in the league, six points behind leaders Liverpool who thrashed Newcastle United 4-0.
Eden Hazard took his tally of goals for Chelsea into three figures, scoring twice in a 2-1 win at Watford as the Blues remained fourth, 11 points behind Liverpool.
Ole Gunnar Solskjaer got his second win as Manchester United manager with a comfortable 3-1 triumph over Huddersfield Town, while Everton smashed five past Burnley to bounce back from their own humbling by Spurs.
But it was City's disappointing result at Leicester that was the most intriguing result, especially since Pep Guardiola's team had taken the lead after Bernardo Silva put them in front before the 15th minute.
The Foxes equalised shortly after to capitalise on the creeping insecurity around the champions, following on from their 3-2 defeat by Crystal Palace at the weekend.
Leicester withstood some usual City pressing and then seized on their own opportunity late on with Ricardo Pereira unleashing an stoppable shot beyond Ederson to take the unlikely win.
City slipped to third after Spurs took their tally to 11 goals in four days by adding Bournemouth to their list of festive thrashings.
Son Heung-min scored twice with Christian Eriksen, Lucas Moura and Harry Kane getting one goal apiece to move up to second.
Liverpool are still six points out in front and remain unbeaten after goals from Dejan Lovren, Mohamed Salah (penalty), Xherdan Shaqiri and Fabinho condemned Newcastle to their 10th defeat of the season.
Chelsea bounced back from a home defeat against Leicester as Hazard scored either side of half time, his second from the spot.
Watford had won two straight, but with the setback slipped to ninth in the table with 27 points.
The match, however, was overshadowed by the injury suffered by Watford defender Christian Kabasele, who crashed into a goalpost early in the game.
Despite appearing to suffer a rib injury in the collision, he tried to continue but ended up being carried out of the ground on a stretcher while being given oxygen.
At the other end of the table, Fulham conceded in the final five minutes against Wolverhampton Wanderers to draw 1-1.
Huddersfield were left in last place as they lost 3-1 to Solskjaer's new look United, who had Paul Pogba to thank for two of their goals and who is finally starting to look like the player the club paid 89 million pounds for.
Everton's new signings came to the fore at Turf Moor as Lucas Digne scored twice and Yerry Mina scored his first goal for the club in a 5-1 thumping of Burnley where Richarlison also notched his ninth goal of the season late on.
The game that was the turkey of the day, however, was the 0-0 draw between Crystal Palace and Cardiff City.
(Reporting by Christian Radnedge; additional reporting by Andrew Both; editing by Pritha Sarkar)
