Erling Haaland had a second-half penalty saved by Jordan Pickford as Manchester City's crisis continued with a laboured Premier League draw against Everton at Etihad Stadium.
Pep Guardiola's side, once all-conquering, are in unfamiliar territory amid a staggering fall-off, with just one win now in their past 13 games in all competitions.
The result leaves the champions sixth in the table, three points adrift of Nottingham Forest in fourth and 11 behind leaders Liverpool, with those two sides still yet to play on Thursday.
City almost made the perfect start in the third minute but Josko Gvardiol's towering header cannoned back off the post - and the hosts were rewarded for their dominance shortly after.
They grabbed a deserved opener in the 14th minute as Bernardo Silva latched on to Jeremy Doku's pass and managed to bobble home a finish into the far corner courtesy of a deflection off Jarrad Branthwaite.
It should have been two when Phil Foden fed a pass to the onrushing Silva inside the box, but the Portugal international sent his first-time attempt wide of the post on this occasion.
But with their first clear-cut chance of the game, Everton drew level in the 36th minute through Iliman Ndiaye's marvellous strike, taking a touch from Abdoulaye Doucoure's cross and sending a delightful finish with the outside of his boot into the far corner.
City had the chance to regain the lead seven minutes into the second half when left-back Vitalii Mykolenko chopped down Savinho inside the area, but Pickford dived the right way to keep out Haaland's spot-kick.
City pushed for the winner but failed to prise open the Everton backline and were left to suffer again, with their last victory coming on 4 December against Forest.
Guardiola led City to the club's greatest moment by claiming the Champions League in 2023 to seal the Treble, but he, his players and the supporters will be content just to win another game at the moment.
The ex-Barcelona and Bayern Munich boss suggested before the match that a top-four finish was "at risk" in their current form, and Thursday's performance suggests they face a tough battle to achieve that feat.
City have competed in Europe's elite club competition for 14 consecutive campaigns and at the start of this term most would have taken it for granted for them to extend that run, but the season has not panned out in such a way and their remarkable decline continues.
Their previous slick play has turned slow and ponderous, which made it easier for Everton to sit back and play against, and their confidence ebbed away after conceding another soft goal with the defence watching on.
It started well as Silva's darting run caught Everton napping and his deflected effort gave City the lead, but they were unable to build on that early goal despite numerous chances.
After scoring the first, Silva's failure to find the net from around 15 yards out proved to be costly as Everton recovered.
Savinho's thunderous volley was kept out by Pickford's sprawling stop at the start of the second half, while Mateo Kovacic flashed a strike narrowly wide before Haaland's gilt-edged chance.
The prolific Norwegian, who has 13 league goals this season, was outpsyched by Pickford for the penalty and though City recycled the ball and Haaland headed in, the flag went up for offside.
Guardiola sent on Kevin de Bruyne and Ilkay Gundogan in an attempt to change his fortunes, but the side were met with a smattering of jeers at the full-time whistle, having now gained only five points since the start of November.
Everton had kept three straight clean sheets coming into this game and although their backline was breached, they have now managed credible consecutive draws against Arsenal, Chelsea and here against City.
Whether their glass is half-full or half-empty at present depends on perspective.
Boss Dyche will point to his side being difficult to beat, having lost only two of their past 13 top-flight matches - but on the other hand, they have won only three of their 17 games so far this season.
This draw leaves them in 15th place, edging five points clear of the relegation zone, and it came through Ndiaye's exquisite effort, which was thoroughly enjoyed by the travelling supporters.
They could have snatched it late on when Orel Mangala's deflected strike wrong-footed Stefan Ortega but the ball drifted the wrong side of the post, leaving Everton the happier side with the result but without a victory against City in their past 16 meetings.