Ellis Simms scored his first Everton goal to earn Sean Dyche's side a precious point as they came from behind twice to draw against Chelsea at Stamford Bridge.
Everton's improved resilience under Dyche was on show again and 22-year-old local product Simms was the hero with a superb late equaliser to wreck Chelsea's hopes of a fourth consecutive win.
Chelsea broke down Everton's resistance seven minutes after the break when the excellent Joao Felix drilled home a low drive, but they were pegged back when Abdoulaye Doucoure scrambled home an equaliser from a corner after 69 minutes.
Everton were only on level terms for seven minutes until Kai Havertz scored from the spot after Reece James was fouled by James Tarkowski - but there was to be a late twist in the tale.
Dyche had put Simms on to rescue a point and he delivered in style with a powerful run and finish a minute from time.Reaction to Chelsea's draw with EvertonHow did you rate Chelsea's performance? Have your say hereWhat did you make of Everton's display? Send us your views here
"A young player coming on and earning his spurs. We know he's got power and pace, then a fine finish under the keeper," Dyche, speaking to BBC Sport, said of Simms.
"I'm really pleased for him. He spoke to me last week, I told him to tell me where he needs to get better. He told me four things and I said 'you're right' - one of them was playing stronger and he did that today."
Simms, who has had loan spells at Blackpool, Hearts and most recently Sunderland, was recalled to Goodison Park in January as then-manager Frank Lampard sought to bolster his attacking options.
He made just one Everton appearance prior to this season but has featured in six games since returning to his boyhood club - including four under Dyche.
Simms told Sky Sports: "It's about patience - I just had to wait for my chance. We've got top players so I'm not going to walk straight into the team. I have to work hard and take my chance when I get it."
Everton's show of strength
Everton's fans celebrated this point like a victory and their elation was justified as they had witnessed the character and fighting spirit Dyche has been injecting into his side.
They kept Chelsea at arm's length until the second half then reacted superbly to going behind twice, especially when they gathered themselves again when all looked lost after Havertz's penalty.
Everton were strong in defence throughout, prepared to throw bodies on the line, and showed their threat from set pieces once again when Doucoure headed in at the far post from a corner.
The high point, however, was the manner in which youngster Simms - back at Everton after a loan spell at Sunderland - outmuscled Kalidou Koulibaly and raced on to beat Chelsea keeper Kepa with a cool finish.
Everton survived a couple of late scares but deserved to do so after a performance that will give them real hope of winning their fight to avoid the drop out of the Premier League.Go straight to our Everton page
Careless Chelsea squander victory chance
Chelsea will be hugely frustrated at the manner in which they allowed Everton to come back twice and take a point away from Stamford Bridge.
Graham Potter's side had control of the game by leading twice but on each occasion Everton fought their way back into contention.
Felix brought class to proceedings and fully merited his goal, but he was substituted late on as Potter adopted a more conservative approach which ultimately failed to secure the desired result.
Chelsea have shown improvement in recent weeks but this was an opportunity missed and stopped their revival in its tracks.
Potter is still navigating his way around adapting to the vast influx of players after Chelsea's transfer spending spree, but this was a bitter disappointment after that recent upturn.All the best Chelsea news and views in one place
Player of the match
with an average of 8.14
Squad number11Player nameJoão Félix
Squad number21Player nameChilwell
Squad number33Player nameFofana
Squad number24Player nameJames
Squad number8Player nameKovacic
Squad number5Player nameFernández
Squad number29Player nameHavertz
Squad number4Player nameBadiashile
Squad number10Player namePulisic
Squad number1Player nameArrizabalaga
Squad number26Player nameKoulibaly
Squad number23Player nameGallagher
Squad number12Player nameLoftus-Cheek
Squad number30Player nameChukwuemeka
Squad number14Player nameChalobah
Squad number50Player nameSimms
Squad number11Player nameGray
Squad number16Player nameDoucouré
Squad number7Player nameMcNeil
Squad number19Player nameMykolenko
Squad number8Player nameOnana
Squad number2Player nameTarkowski
Squad number23Player nameColeman
Squad number17Player nameIwobi
Squad number22Player nameGodfrey
Squad number5Player nameKeane
Squad number1Player namePickford
Squad number27Player nameGueye
Formation 3-4-31Arrizabalaga33FofanaSubstituted forChalobahat 87'minutes26KoulibalyBooked at 57mins4Badiashile24JamesBooked at 74mins5Fernández8KovacicSubstituted forLoftus-Cheekat 81'minutes21Chilwell10PulisicSubstituted forGallagherat 62'minutes29Havertz11João FélixSubstituted forChukwuemekaat 86'minutes
Formation 4-5-11Pickford23ColemanSubstituted forMykolenkoat 84'minutes5Keane2Tarkowski22Godfrey17Iwobi16Doucouré27GueyeBooked at 29minsSubstituted forSimmsat 79'minutes8Onana7McNeilBooked at 45mins11Gray
Match ends, Chelsea 2, Everton 2.
Second Half ends, Chelsea 2, Everton 2.
Corner, Chelsea. Conceded by James Tarkowski.
Attempt blocked. Benoît Badiashile (Chelsea) header from very close range is blocked. Assisted by Ben Chilwell with a cross.
Corner, Chelsea. Conceded by Ben Godfrey.
Attempt blocked. Kai Havertz (Chelsea) with an attempt from very close range is blocked. Assisted by Reece James with a cross.
Reece James (Chelsea) wins a free kick on the right wing.
Foul by Dwight McNeil (Everton).
Corner, Chelsea. Conceded by Dwight McNeil.
Goal! Chelsea 2, Everton 2. Ellis Simms (Everton) right footed shot from the left side of the box to the bottom right corner. Assisted by Abdoulaye Doucouré.
Ben Chilwell (Chelsea) wins a free kick in the defensive half.
Foul by Demarai Gray (Everton).
Substitution, Chelsea. Trevoh Chalobah replaces Wesley Fofana.
Substitution, Chelsea. Carney Chukwuemeka replaces João Félix.
Attempt blocked. Ellis Simms (Everton) right footed shot from outside the box is blocked.
Substitution, Everton. Vitalii Mykolenko replaces Séamus Coleman.
Attempt missed. Dwight McNeil (Everton) left footed shot from the left side of the box is close, but misses to the right. Assisted by Abdoulaye Doucouré.
Substitution, Chelsea. Ruben Loftus-Cheek replaces Mateo Kovacic.
Reece James (Chelsea) wins a free kick in the defensive half.
Foul by Amadou Onana (Everton).
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