Crouch was unable to avoid putting the ball in his own net on the stroke of half-time and Jerome had an immediate impact just 90 seconds after coming on as a substitute, levelling the score in the 69th minute.
Both sides went for the win but it remained all square, with Everton stretching their unbeaten run in the league to seven games and strengthening their hold on seventh position in the table as Liverpool lost to Fulham. A point for Stoke moved Tony Pulis’s side one place up to 13th in the standings.
There were chances from the very start as Stoke caused David Moyes’s team problems from a couple of long Rory Delap throws, and Sylvain Distin almost placed a perfect cross from the left onto the head of the in-form Nikica Jelavic as both teams pressed one another.
Everton lost Victor Anichebe to injury after just 20 minutes when the striker landed awkwardly after going up for a header, but his replacement Magaye Gueye proved a capable deputy as he continued the link-up with the lively Steven Pienaar that Anichebe had established early on. The Frenchman was himself forced off injured in the second half however.
Leon Osman had a strong shot saved by Asmir Begovic as Everton slowly increased the pressure and there were more Delap throws to trouble the Everton defence. Jelavic was caught out by a Gueye cross from the left that surprised the striker, who was unable to keep a snap-shot down.
Pienaar forced Begovic to tip over the crossbar as the visitors upped the ante heading towards the interval, and right on the stroke of half-time they took the lead. A cross from Tony Hibbert resulted in the ball being cannoned around the six-yard area, and the unfortunate Crouch was unable to avoid putting the ball past his own goalkeeper when it came off his left shoulder.
After Everton had ended the first half in the ascendancy Stoke began the second stronger, but it was the away side who went closest to scoring. Osman shot straight at Begovic as he had done in the first half, and Stoke then put their foot on the gas.
With his team piling the pressure on Pulis made a triple substitution, sending on Jerome, Ricardo Fuller and Glenn Whelan, and the impact was instant.
Jerome latched onto a ball forward, held off Phil Jagielka and Johnny Heitinga and then sent a shot past Tim Howard with the aid of a slight deflection off Jagielka.
Everton went close to taking the lead again, Osman guilty of a miss from close range when he sliced wide, and Robert Huth’s free-kick right on the final whistle was saved by Howard via a deflection as Stoke almost stole it at the very end.