Chelsea missed a chance to move two points behind Premier League leaders Manchester City as a depleted Everton side earned a superb point at Stamford Bridge.
England midfielder Mason Mount gave the hosts a deserved lead in the 70th minute with a calm finish past Everton goalkeeper Jordan Pickford following Reece James' pass.
But Everton equalised four minutes later when 19-year-old defender Jarrad Branthwaite, in his first league appearance of the season, converted at the back post after Anthony Gordon's free-kick.
Thiago Silva had a chance to win it for the hosts but saw his powerful header superbly saved by Pickford.
It was an impressive performance from the England international as he also kept out earlier efforts from Christian Pulisic, James, Jorginho and three strikes from Mount when it was goalless.
Two points dropped for Chelsea, but Everton fight hard for point
Chelsea, aiming to win the Premier League title for the first time since 2016-17, will be left wondering how they failed to get the three points in a match where they had 80% possession and had 23 shots.
The result leaves them third, four points behind leaders City, with Everton staying 14th.
But Rafael Benitez, back at Stamford Bridge after a spell as Chelsea manager in 2012-13, will have been delighted with the effort and desire from his Everton side, who were without 12 players because of injury or illness.
Chelsea 1-1 Everton: Players did 'everything they could' to get 'great' point - BenitezThe Spaniard had to make five changes from the weekend, with Demarai Gray, Salomon Rondon and Fabian Delph ruled out because of illness, while Richarlison and Andros Townsend had joined a lengthy injury list, which already included Dominic Calvert-Lewin, Tom Davies and Yerry Mina.
That led to Benitez handing a first-team debut to 20-year-old striker Ellis Simms, with Branthwaite making only his second Everton appearance.
Before the match, Chelsea boss Thomas Tuchel confirmed that strikers Romelu Lukaku and Timo Werner, as well as winger Callum Hudson-Odoi, had tested positive for Covid-19, while another forward, Kai Havertz, was also not in the squad while awaiting a Covid test result.
Chelsea 1-1 Everton: Everton draw 'hard to swallow' for Chelsea - TuchelChelsea missed those strikers as they were regularly frustrated by Pickford, with Mount and James shooting just wide and the impressive Hakim Ziyech narrowly missed the target on three occasions.
It was a similar situation after the break with Mount, Ruben Loftus-Cheek, Cesar Azpilicueta and Antonio Rudiger all missing chances as the home fans became restless.
Mount's goal settled their nerves but Everton showed superb character to equalise four minutes later with Gordon's free-kick from deep finding Branthwaite, sliding in, to snatch a leveller.
Player of the match
BranthwaiteJarrad Branthwaite
Chelsea
Squad number19Player nameMount
Squad number24Player nameJames
Squad number6Player nameThiago Silva
Squad number2Player nameRüdiger
Squad number16Player nameMendy
Squad number22Player nameZiyech
Squad number10Player namePulisic
Squad number12Player nameLoftus-Cheek
Squad number28Player nameAzpilicueta
Squad number5Player nameJorginho
Squad number3Player nameAlonso
Squad number14Player nameChalobah
Squad number18Player nameBarkley
Squad number17Player nameSaúl
Everton
Squad number32Player nameBranthwaite
Squad number1Player namePickford
Squad number24Player nameGordon
Squad number61Player nameDobbin
Squad number22Player nameGodfrey
Squad number5Player nameKeane
Squad number50Player nameSimms
Squad number62Player nameOnyango
Squad number16Player nameDoucouré
Squad number2Player nameKenny
Squad number25Player nameGbamin
Squad number21Player nameAndré Gomes
Squad number4Player nameHolgate
Squad number17Player nameIwobi
Line-ups
Chelsea
Formation 3-4-2-1
16Mendy
28Azpilicueta6Thiago Silva2Rüdiger
24James12Loftus-Cheek5Jorginho3Alonso
19Mount22Ziyech
10Pulisic
16Mendy28AzpilicuetaSubstituted forChalobahat 79'minutes6Thiago Silva2Rüdiger24James12Loftus-CheekBooked at 45minsSubstituted forBarkleyat 65'minutes5JorginhoBooked at 59mins3AlonsoSubstituted forSaúlat 65'minutes19Mount22Ziyech10PulisicSubstitutes
1Arrizabalaga4Christensen7Kanté13Bettinelli14Chalobah17Saúl18Barkley31SarrEverton
Formation 5-4-1
1Pickford
2Kenny4Holgate5Keane32Branthwaite22Godfrey
17Iwobi16Doucouré21André Gomes24Gordon
50Simms
1Pickford2Kenny4HolgateBooked at 21mins5Keane32Branthwaite22Godfrey17Iwobi16Doucouré21André GomesBooked at 64minsSubstituted forGbaminat 71'minutes24GordonSubstituted forOnyangoat 90'minutes50SimmsSubstituted forDobbinat 62'minutesBooked at 77minsSubstitutes
6Allan15Begovic23Coleman25Gbamin31Lonergan61Dobbin62OnyangoReferee:Michael OliverAttendance:13,933Live Text
Match ends, Chelsea 1, Everton 1.
Second Half ends, Chelsea 1, Everton 1.
Substitution, Everton. Tyler Onyango replaces Anthony Gordon.
Foul by Hakim Ziyech (Chelsea).
Abdoulaye Doucouré (Everton) wins a free kick in the attacking half.
Foul by Reece James (Chelsea).
Lewis Dobbin (Everton) wins a free kick in the defensive half.
Corner, Chelsea. Conceded by Jarrad Branthwaite.
Attempt missed. Christian Pulisic (Chelsea) header from the centre of the box misses to the left. Assisted by Reece James with a cross following a set piece situation.
Jorginho (Chelsea) wins a free kick on the right wing.
Foul by Anthony Gordon (Everton).
Attempt saved. Antonio Rüdiger (Chelsea) header from the centre of the box is saved in the top centre of the goal. Assisted by Mason Mount with a cross.
Corner, Chelsea. Conceded by Jordan Pickford.
Attempt saved. Thiago Silva (Chelsea) header from the centre of the box is saved in the bottom left corner. Assisted by Ross Barkley with a cross.
Substitution, Chelsea. Trevoh Chalobah replaces César Azpilicueta.
Corner, Chelsea. Conceded by Ben Godfrey.
VAR Decision: No Penalty Everton.
Lewis Dobbin (Everton) is shown the yellow card.
Lewis Dobbin (Everton) has gone down, but the referee deems it simulation.
Corner, Everton. Conceded by Thiago Silva.
Our coverage of your Premier League club is bigger and better than ever before - here's everything you need to know to make sure you never miss a moment