Chelsea stretched their unbeaten Premier League start to 12 games but had to settle for a point after failing to breach Everton during a goalless draw at Stamford Bridge.
Maurizio Sarri's side were nullified by disciplined visitors during the first half but the scoreline belied their dominance after the interval as Jordan Pickford, the goalframe and the offside flag left them frustrated.
Marcos Alonso had the game's best chances but though the stage seemed set for Ross Barkley against his former club, the late substitute could only lash wide from distance and a home breakthrough remained elusive.
The Blues would have returned to the summit, for a few hours at least, but the result leaves them third in the table behind Manchester City and Liverpool, with Everton staying in ninth place.
Sarri will rue the missed opportunity but his start to Premier League management is now a record one, the Italian surpassing Frank Clark's 11 unbeaten run with Nottingham Forest from August to October 1994.
Chelsea: Arrizabalaga (6), Azpilicueta (7), Rudiger (7), Luiz (6), Alonso (7), Kante (6), Jorginho (6), Kovacic (7), Willian (6), Morata (5), Hazard (7).
Subs: Fabregas (6), Barkley (6), Pedro (6).
Everton: Pickford (7), Coleman (7), Keane (7), Mina (8), Digne (7), Andre Gomes (6), Gueye (7), Walcott (6), Sigurdsson (7), Bernard (6), Richarlison (6).
Subs: Jagielka (6), Lookman (6), Calvert-Lewin (n/a).
Man of the match: Yerry Mina
After the Chelsea Pensioners had led remembrance tributes, the visitors to west London started brightest on the pitch, Andre Gomes heading narrowly over and Bernard fizzing wide following threatening Lucas Digne deliveries.
A ball over the top narrowly evaded Alvaro Morata's lunge but Chelsea continued to be thwarted by well-drilled opponents, as well as by Everton goalkeeper Pickford when Yerry Mina's foul on Eden Hazard gave Alonso a dead-ball chance.
The sides had failed to muster a shot on target as the break loomed but Alonso lashed a venomous first (41) when he peeled away to meet Willian's free-kick on the volley, the angle tight but Pickford forced to palm away.
Ross Barkley was named as a substitute as Chelsea made eight changes to the side which began the win at BATE Borisov on Thursday, with Kepa Arrizabalaga, Jorginho and Eden Hazard the players retained.
Richarlison shrugged off an ankle injury to start for Everton, with Colombia defender Yerry Mina making his full debut.
Morata's hopeful penalty appeal was dismissed before a flashpoint between Bernard and Antonio Rudiger saw both players booked as the half ended with a frisson but still no breakthrough.
Pickford was called upon again just seconds after the restart, Morata under pressure from Mina but almost converting Hazard's lofted cross, and as the game opened up, Kepa Arrizabalaga tipped over from Gylfi Sigurdsson.
As Barkley warmed up to some jeers from the travelling supporters, Willian dithered and then fired wide, while Pickford scrambled to push over Hazard's deflected shot in a breathless passage of play.
Alonso drilled against the far post (65) as a Chelsea opener impossibly remained elusive but Morata could have no complaints when he tapped in soon after but saw the offside flag.
The Spaniard was further aggrieved when a tussle with Michael Keane brought no Everton punishment and a flurry of substitutes were made in vain, Barkley's entrance promising but failing to deliver late drama.
- Chelsea have remained unbeaten after their opening 12 games to a season in the top-flight for only the second time, also doing so in 2014-15 when they went on to win the Premier League.
- Chelsea and Everton have now played out eight goalless draws in the Premier League; only Everton v Liverpool (nine) has seen more in the competition's history.
- Everton are now winless in their last 24 Premier League visits to Chelsea (D11 L13), their outright second longest run without a win away at any opponent in their league history after a 36-game streak at Leeds United between April 1953 and December 2001.
- This was Chelsea 21st Premier League clean sheet against Everton; against no other opponent have they managed more in the competition (also 21 v Newcastle United and Tottenham Hotspur.
- This was Everton manager Marco Silva's first goalless draw in the Premier League since August 2017 with Watford against Brighton, having previously gone 32 games without one in the league.
Man of the match - Yerry Mina
The Colombia international posted some impressive stats on his full debut and boss Marco Silva was impressed. "He showed his quality," Silva said. "Even without the ball he did what we planned in terms of our defensive organisation and process." Mina might have caught Hazard with a meaty challenge that Sky Sports' Graeme Souness thought fortunate to bring yellow rather than red but he was a vital robust presence as Chelsea failed to score at home for the first time this season.
With international duties to fulfill over the night fortnight, Chelsea are next back in Premier League action in a London derby at Tottenham on November 24, with Everton hosting Cardiff the same day.