Everton moved two points clear of the drop zone as Simms’ first senior goal secured a valuable point against Chelsea.
Chelsea broke down Everton’s resistance in the 52nd minute 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 James Tarkowski headed the ball towards him on 69 minutes.
Everton were only on level terms for seven minutes before Kai Havertz coolly scored from the spot after Reece James was fouled by James Tarkowski – but there was to be a late twist in the tale.
Sean Dyche had put Simms on to rescue a point and he delivered in style with a powerful run past Kalidou Koulibaly and finish a minute from time.
It was the 22-year-old local’s first goal for the Toffees and the away stands erupted in rapturous joy.
Even though Chelsea failed to make it four straight wins, they kept on the record that has seem them unbeaten at home to Everton in the Premier League since 1994.
The Blues, who started the game in 11th, had the chance to move to 9th but are now back in 10th.