Ellis Simms scored his first Everton goal in the 89th minute at Stamford Bridge to claim a vital point in the Toffees' relegation fight and halt Chelsea's recent resurgence
Chelsea had bounced back from a horrendous run of form at the start of the year by winning their last three matches in all competitions and they should have made it four in a row after twice taking the lead against Everton
Joao Felix rolled the Blues' first past Jordan Pickford via the post seven minutes after the break only for the hosts to allow complacency to creep into their game, resulting in Abdoulaye Doucoure glancing a header just over the line to level for the visitors in the 69th minute
Chelsea managed to hit back through Kai Havertz seven minutes later when he converted a penalty after a foul on Reece James, but the Blues again threw it away, with Simms easily bursting past Kalidou Koulibaly before seeing his shot squirm past Kepa Arrizabalaga as the Toffees continued their spirited fight against the drop
After appearing to be careering towards relegation under former Chelsea boss Frank Lampard at the end of January, Everton’s revival under Dyche continued in west London thanks to another impressively gritty performance
The Toffees took just two points from their final eight Premier League games under Lampard but have earned 11 from Dyche’s first eight matches in charge, a clear demonstration of the positive impact the former Burnley boss has made
Everton frustrated Chelsea throughout their Saturday evening encounter, with a defender seemingly in the way of the ball every time it went near Pickford’s goal during a first half of few clear chances
The visitors’ resistance was finally breached by Felix after he collected Michael Keane’s weak clearance to guide the ball into the far corner but Everton’s battling qualities were on display as they fought back to level through Doucoure, who turned James Tarkowski’s header past Kepa from close range
A rare mistake from Tarkowski and Ben Godfrey, who combined to trip James, allowed Havertz to score his third goal in as many games from the spot, but Everton were not to be denied as Simms charged into the Chelsea area and ended their three-game winning run
The result moves Dyche’s side up to 15th and two points clear of the drop zone, while Graham Potter’s team missed the chance to close the gap on fourth-placed Tottenham and lie 10th, 11 points off the top four
It’s far too early to anoint Simms as Everton’s answer at No 9 but the way in which the 22-year-old announced his arrival onto the scene was a welcome boost for the goal-shy Toffees
Only Crystal Palace have scored fewer Premier League goals than Everton’s 22 this season and with Dominic Calvert-Lewin apparently unable to stay fit and Neal Maupay out of favour, Dyche has felt the need to start Demarai Gray, a winger, as his striker in recent weeks
But Simms, recalled from a productive loan spell at Sunderland in January, showed he could play a pivotal role in the closing stages of Everton’s campaign during his cameo against Chelsea
With 11 minutes to go and his side staring defeat in the face, Simms was thrown on to try to save the game for Everton - and he did just that
The way in which Simms breezed past Koulibaly - one of Europe’s standout centre-backs before joining Chelsea - was striking and, while Kepa could perhaps have done better in trying keep out his effort, Simms deserves credit for getting his shot on target and ultimately showing his fellow forwards how to find the back of the net
Dyche chose to praise his players for avoiding defeat away from Goodison Park for the second match in succession following a run of four defeats in a row away from home
Speaking to , the Everton boss said: "I'm really pleased with the growth in mentality
 There's been a lot of questions about Everton's away form and the mentality around that but it's been improving all the time
“It's still a tough place to come here
 I know they've [Chelsea] been up and down but they're a good outfit, coming off of three wins
"We showed them a little bit too much respect in the first half but after that we got back to grips with the game and reacted well to going behind twice
"Potter was frustrated with the way in which Everton scored their goals, saying: "We’re really disappointed because we’ve dropped two points at home
"There was a lot of positive things in the performance but ultimately we haven’t defended well enough
"Most of the game we controlled fairly well - as much as you can at this level - but the first goal is really disappointing from a set-piece perspective and we spoke about that before the game
"The second goal we haven’t attacked well enough and exposed ourselves to a big space to defend
 To be cheap with the goals we conceded is frustrating
"Chelsea’s three-game winning run relieved the pressure on Potter at the opportune time after his job was seemingly on the brink following a run of one win in 11 matches in all competitions, but nobody should have been fooled into thinking the manager has fixed all his side’s problems
While Potter is finally getting a tune from his forward line following a profligate start to the year, Chelsea still lack a ruthless streak, too often failing to finish off opponents when they’re there for the taking
The Blues deserve credit for  at the start of the month and , but both results were only secured after nervy endings
 last weekend but they were guilty of  last month and they can only have themselves to blame for repeating the trick against Everton
Potter admitted after the game that his side’s defending was sloppy and he will know Chelsea cannot afford to continue making the same mistakes if they have any hope of returning to the Champions League next season
The Premier League now pauses for the international break, meaning next game is at home to in the top flight on Saturday April 1, live on  - kick-off 5
30pm
The Blues then host on Tuesday April 4, live on  - kick-off 8pm
next game is at home to in the Premier League on Monday April 3, live on  - kick-off 8pm
The Toffees then travel to on Saturday April 8 - kick-off 12
30pm
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