Chelsea s English midfielder Conor Gallagher (C) fights for the ball Everton s Senegalese midfielder Idrissa Gueye (L) and Everton s English defender Michael Keane during the English Premier League football match between Chelsea and Everton at Stamford Bridge in London on March 18, 2023. AFP
Sean Dyche's side were moments away from a damaging defeat until Simms scored his first goal for the club to stun Stamford Bridge into silence.
Everton's show of defiance came after they twice trailed in west London.
Joao Felix had put Chelsea ahead early in the second half with his second goal since joining on loan from Atletico Madrid in January.
Abdoulaye Doucoure's equaliser was followed by Kai Havertz's third goal in his last three appearances as the German converted penalty in the closing stages.
Simms was on loan at Championship side Sunderland earlier this season, but the 22-year-old showed he could be Everton's saviour in the relegation battle with his crucial leveller.
Everton are now two points clear of the relegation zone after extending their unbeaten run to three games.
It was a bitter pill for Chelsea to swallow as Graham Potter's team squandered the chance to clinch a fourth successive win in all competitions.
The match was marred by homophobic chanting from Everton fans, who could be heard singing "Chelsea rent boy".
It was announced in January that clubs could be charged by England's Football Association if their fans sang the offensive song.
The UK's Crown Prosecution Service defined the term as a hate crime last year.
That was an ugly side to a memorable match that started with Chelsea's Mateo Kovacic volleying just wide from the edge of the area.
Chelsea were monopolising possession but Jordan Pickford kept Everton on level terms with a brave save as the keeper dived to block at Felix's feet.
Felix, a constant menace with his quick feet and clever movement, forced Pickford to save his effort from 18 yards.
Hampered all season by a lack of cutting edge, Chelsea had scored more than once in just two games in all competitions in 2023.
Sting in the tale
Netting three times at Leicester in their previous match had given Potter encouragement that he had solved Chelsea's attacking woes.
There was undoubtedly more vibrancy about Chelsea and Felix rewarded their territorial dominance in the 52nd minute.
When Ben Chilwell's cross deflected to Felix just inside the Everton area, the Portugal star seized his chance with a low drive that beat Pickford and cannoned into the net off the far post.
Felix's first goal in seven games was nearly followed by an Everton equaliser moments later when Michael Keane headed wide from Demarai Gray's free-kick.
It was a warning Chelsea failed to heed as Everton equalised in the 69th minute.
Conjuring a goal straight from the Dyche playbook, Everton struck from Dwight McNeil's corner as Ben Godfrey flicked on and Doucoure nodded home from close range before Havertz could clear off the line.
Chelsea were back in front seven minutes later as Reece James' run was halted by Godfrey's trip and an equally clumsy challenge from James Tarkowski in the area.
Havertz scored a crucial penalty in the Champions League last-16 win against Borussia Dortmund recently and he coolly sent Pickford the wrong way from the spot for his ninth goal this season.
But there was a sting in the tale in the 89th minute as Doucoure picked out Simms' surge into the Chelsea area.
The striker shrugged off Kalidou Koulibaly's weak challenge and hit a low shot that crept under Kepa Arrizabalaga to salvage a point in heart-stopping fashion.
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