Everton's Premier League survival hopes were given a huge boost as Richarlison struck the only goal of the game to beat a lacklustre Chelsea at Goodison Park.
The Brazilian took full advantage of an uncharacteristic mistake from Cesar Azpilicueta to give the Toffees the lead immediately after the restart, as Frank Lampard's side held on to move to within two points of safety.
There was little in the way of goalmouth action in the first half but an abundance of endeavour and passion, particularly from the Everton players, as five yellow cards were shown before half-time.
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Although they failed to register a shot on target in the opening 45 minutes, Chelsea went closest to breaking the deadlock, Mason Mount's dipping effort from distance clipping the roof of the net.
The first goal was always going to be crucial, and it arrived just a minute after the restart when Richarlison picked the pocket of Azpilicueta, and the Brazilian kept his composure to slot it past Edouard Mendy and send the Everton supporters into raptures.
It could have got even better for the Toffees moments later when Vitalii Mykolenko was played through by Abdoulaye Doucoure but the full-back failed to hit the target as a huge chance went begging.
At the opposite end, Jordan Pickford pulled off two incredible saves to keep Everton's clean sheet intact, somehow denying Azpilicueta after Mount's half-volley struck the post and blocking Antonio Rudiger's point-blank shot from the resulting set-piece.
A fearless Everton continued to throw bodies forward in search of a killer second, as Demarai Gray and Anthony Gordon went close. But the hosts crawled back into their shell as an agonising seven minutes were added on, and Pickford was required once more to save from Mateo Kovacic.
The relief was palpable as the final whistle sounded as Lampard's men earned a priceless victory. Everton remain in the bottom three but are now just two points behind Burnley and Leeds, in 16th and 17th respectively, with a game in hand over their rivals.
Chelsea stay third, just three points ahead of fifth-placed Arsenal ahead of their trip to West Ham later on Sunday, as the race for the top-four heats up.
TALKING POINT - Huge result that could have ramifications at both ends of the table
Cheered on by their raucous supporters, Everton have claimed what is a huge victory at the bottom of the table, a result that keeps their top-flight status in their own hands. After Burnley's victory over Watford on Saturday, the pressure was heaped on the Toffees but they upped their game and were deserving winners, and could have been out of sight long before the fourth official indicated an extraordinary seven minutes were going to be added on.
Could this be a defining afternoon for Frank Lampard's men in their battle against the drop? Aside from the game in hand, they have an arguably kinder run-in than their rivals and their home form of late has been brilliant. Today's victory will only add to the belief that Everton will extend their top-flight status to 69 years.
This result could also have ramifications in the race for the Champions League places next season. Chelsea's worrying run of form continues - they have only won one of their last four league games - and have Arsenal and Tottenham breathing down their neck. Thomas Tuchel needs an immediate response from his players.
MAN OF THE MATCH - Jordan Pickford (Everton)
The England No. 1 underlined his importance to the Toffees with two most impressive saves, moments that will go down in folklore amongst the Goodison Park faithful should Everton survive.
Everton: Pickford 9*, Holgate 7, Mina 7, Mykolenko 7, Coleman 8, Delph 7, Doucoure 7, Gray 7, Iwobi 7, Gordon 7, Richarlison 8.. subs: Allan 6, Rondon 6, Alli N/A.
Chelsea: Mendy 7, Rudiger 5, Alonso 5, Silva 6, Azpilicueta 4, James 6, Jorginho 4, Loftus-Cheek 7, Mount 6, Havertz 6, Werner 5.. subs: Kovacic 5, Pulisic 5, Ziyech 6.
46' - GOAL! EVERTON 1-0 CHELSEA (RICHARLISON): What a huge goal at the bottom of the Premier League table! Everton have got their noses in front at the start of the second half! It's a rare mistake in the Chelsea defence as Azpilicueta is too passive and is quickly closed down by Richarlison who keeps his composure to slot it past Mendy.
49' - ANOTHER HUGE CHANCE FOR EVERTON! The Toffees carve Chelsea's defence open and really Mykolenko should double their lead! Doucoure spots the run of the full-back and releases a perfectly weighted pass, but credit to Mendy who narrows the angle and Mykolenko fails to hit the target from point-blank range!
58' - WHAT A SAVE! Mount's half-volley crashes off the post but Pickford is quickly back to his feet and somehow keeps out Azpilicueta's shot on the rebound. Incredible from the England No. 1, and how crucial could that prove to be?
59' - PICKFORD TO THE RESCUE, AGAIN! Wow, Jordan Pickford, take a bow! Rudiger is left unmarked at the back post from the resulting corner but the Everton goalkeeper somehow blocks his goalbound shot.
90'+2 - PICKFORD SAVES! This could be a long seven minutes for Lampard and Everton, and here comes Chelsea again, Kovacic closing in on goal but again there's no way past a stubborn Pickford!
- Coming into the match against Everton, Chelsea had only trailed for 29 minutes away from home in the Premier League this season, with Richarlison's goal after 46 minutes today more than doubling their season total (73 minutes trailing on the road).
- Richarlison has scored in the first minute of the second half for the third time in the Premier League; in the competition's history, the only player to do so more often is Alan Shearer (four times).
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