Everton moved to within two points of the Premier League safety zone with a priceless win over Chelsea that was inspired by a thunderous atmosphere at Goodison Park.
Starting the day in the relegation places, five points behind Leeds and Burnley, the hosts were lifted by their fans in their attempt to extend a 58-year stay in the top flight.
Everton's aggressive pressing was eventually rewarded a minute after the break when Richarlison's dispossessed Cesar Azpilicueta on the edge of the area and scored his ninth goal of the season.
The Brazilian celebrated by picking up a flare that had landed on to the pitch and throwing it back towards the stand.
Vitalii Mykolenko could have doubled the lead soon afterwards but skewed wide, and Everton were indebted to two stunning saves from Jordan Pickford to keep themselves in front.
First, the Everton keeper denied Azpilicueta after Mason Mount's shot hit both posts and spun out. From the resulting corner, Pickford then took Antonio Rudiger's shot fully in his face, needing medical treatment.
It was an incredible effort from the England stopper, who also saved from Ruben Loftus-Cheek, but typified Everton's approach as they dug in to thwart Thomas Tuchel's side, even if that raw approach drew complaints from the German.
Demarai Gray and Anthony Gordon could have made the game safe late on, but Frank Lampard saw his side hold out against his former employers, to earn only his fourth win in 13 Premier League games in charge.
The victory was vital, reducing the gap behind Leeds and Burnley, with the Toffees having a game in hand on their relegation rivals.
Chelsea, meanwhile, will rue the fact they could not turn their possession into goals, with their preparations hampered by fireworks being set off during the night outside their hotel.
Tuchel said they had not affected his team's preparations, but was left to reflect on a defeat that could hamper their chances of finishing third. Arsenal can climb to within three points of them by winning at West Ham later on Sunday.
Everton earn famous win with full-blooded approach
If Everton and their fans were attempting to rattle their opponents, it worked, for what could prove to be a crucial step towards safety.
With so much at stake, once again the supporters helped boost a struggling but spirited team to earn a third win in four home matches, which will be key to their chances of survival.
Chelsea's build-up had been disrupted, with midfielder Jorginho admitting he was woken by the fireworks outside the Chelsea hotel on Saturday night.
Before kick-off, thousands of Everton fans lined the streets outside Goodison Park, attempting to lift the mood that had been dampened by relegation rivals Burnley's 2-1 victory at Watford on Saturday.
And in a full-blooded match, that noise helped set the tone as the hosts tore into their opponents with an aggression which was met with approval from their fans.
At times, it spilled over. Fabian Delph was fortunate not to go in the book for a foul on Jorginho, and then did shortly before half-time with a late challenge on Mount.
Seamus Coleman and Yerry Mina, back in the side, unsettled Azpilicueta, who was also booked after taking issue with Everton's Colombian defender. Tuchel was furious with some of the treatment handed out to his players on his first visit to Goodison Park.
The football on show was limited in the first half, but it did not deter from a raucous occasion.
Mount curled an effort over after eight minutes. Loftus-Cheek, who replaced N'Golo Kante in midfield, made some dangerous runs from deep, and Gordon was a lively presence, shooting wide of the near post with a left-footed effort.
But no sooner had fans taken their seats for the second half, Everton went ahead and it was a goal made as a result of their tactics.
Azpilicueta dawdled on the edge of the penalty box, allowing Richarlison to pinch the ball from him, receive it back from Gray and slot in at the Gwladys Street End to send the stadium into ecstasy.
Three minutes later, Mykolenko hit the side netting from close range.
But around the hour mark, the home fans were rewarded with more good defensive play from their team, which was cheered as strongly as if Everton had scored.
Mount's initial effort somehow stayed out after he hit both posts, before Pickford produced the first of two miraculous saves, firstly to deny Azpilicueta who had the goal at his mercy.
From the resulting corner, Pickford blocked Rudiger's point-blank effort to keep his goal intact.
Following that commotion, and with Chelsea desperately searching for an equaliser, the game opened up, leading to further chances for Gordon and Richarlison.
Pickford was called into further action to deny Loftus-Cheek. But after seven minutes of stoppage time, the relief and delight inside Goodison was almost tangible as Lampard and his players celebrated a famous win.
Player of the match
RicharlisonRicharlison
Everton
Squad number7Player nameRicharlison
Squad number1Player namePickford
Squad number36Player nameAlli
Squad number33Player nameRondón
Squad number6Player nameAllan
Squad number11Player nameGray
Squad number23Player nameColeman
Squad number13Player nameMina
Squad number24Player nameGordon
Squad number16Player nameDoucouré
Squad number19Player nameMykolenko
Squad number17Player nameIwobi
Squad number4Player nameHolgate
Squad number8Player nameDelph
Chelsea
Squad number19Player nameMount
Squad number12Player nameLoftus-Cheek
Squad number16Player nameMendy
Squad number6Player nameThiago Silva
Squad number24Player nameJames
Squad number2Player nameRüdiger
Squad number11Player nameWerner
Squad number29Player nameHavertz
Squad number3Player nameAlonso
Squad number5Player nameJorginho
Squad number28Player nameAzpilicueta
Squad number8Player nameKovacic
Squad number22Player nameZiyech
Squad number10Player namePulisic
Line-ups
Everton
Formation 5-4-1
1Pickford
17Iwobi23Coleman13Mina4Holgate19Mykolenko
24Gordon16Doucouré8Delph11Gray
7Richarlison
1Pickford17Iwobi23ColemanBooked at 38mins13Mina4HolgateBooked at 90mins19Mykolenko24Gordon16Doucouré8DelphBooked at 45minsSubstituted forAllanat 71'minutes11GraySubstituted forAlliat 90+4'minutes7RicharlisonSubstituted forRondónat 80'minutesSubstitutes
2Kenny5Keane6Allan9Calvert-Lewin15Begovic26Davies32Branthwaite33Rondón36AlliChelsea
Formation 3-4-1-2
16Mendy
28Azpilicueta6Thiago Silva2Rüdiger
24James5Jorginho12Loftus-Cheek3Alonso
19Mount
29Havertz11Werner
16Mendy28AzpilicuetaBooked at 38minsSubstituted forPulisicat 68'minutes6Thiago Silva2RüdigerBooked at 17mins24James5JorginhoSubstituted forKovacicat 45'minutes12Loftus-Cheek3AlonsoBooked at 76mins19MountBooked at 36mins29HavertzBooked at 83mins11WernerSubstituted forZiyechat 68'minutesSubstitutes
1Arrizabalaga8Kovacic9Lukaku10Pulisic14Chalobah17Saúl22Ziyech23Kenedy31SarrReferee:Kevin FriendAttendance:39,256Live Text
Match ends, Everton 1, Chelsea 0.
Second Half ends, Everton 1, Chelsea 0.
Mason Holgate (Everton) is shown the yellow card.
Offside, Chelsea. Hakim Ziyech tries a through ball, but Thiago Silva is caught offside.
Reece James (Chelsea) wins a free kick in the attacking half.
Foul by Dele Alli (Everton).
Attempt blocked. Reece James (Chelsea) right footed shot from outside the box is blocked. Assisted by Mateo Kovacic.
Substitution, Everton. Dele Alli replaces Demarai Gray.
Attempt saved. Mateo Kovacic (Chelsea) right footed shot from the centre of the box is saved in the bottom left corner. Assisted by Marcos Alonso.
Corner, Everton. Conceded by Édouard Mendy.
Attempt saved. Anthony Gordon (Everton) left footed shot from the left side of the box is saved in the bottom left corner. Assisted by Abdoulaye Doucouré.
Attempt blocked. Mateo Kovacic (Chelsea) left footed shot from the left side of the box is blocked. Assisted by Marcos Alonso.
Corner, Chelsea. Conceded by Séamus Coleman.
Attempt missed. Demarai Gray (Everton) right footed shot from the centre of the box is just a bit too high. Assisted by Abdoulaye Doucouré.
Kai Havertz (Chelsea) is shown the yellow card.
Foul by Kai Havertz (Chelsea).
Jordan Pickford (Everton) wins a free kick in the defensive half.
Substitution, Everton. Salomón Rondón replaces Richarlison because of an injury.
Corner, Chelsea. Conceded by Jordan Pickford.
Attempt saved. Ruben Loftus-Cheek (Chelsea) left footed shot from outside the box is saved in the top centre of the goal. Assisted by Reece James.