- 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 straight win.
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 straight 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.
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.
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 the recent upturn.