Other than a Matthew Etherington effort that flew over from just outside the area, Delap was the source of all of Stoke's first-half opportunities, with Robert Huth, Ryan Shawcross and Kenwyne Jones all failing to make the most of opportunities from the former Republic of Ireland international.
Pulis praises 'fantastic' Stoke
Everton lost Victor Anichebe, who had a penalty appeal turned down after a Huth challenge, to injury but his replacement Magaye Gueye immediately gave them plenty of thrust down the left.
The French youngster's cross was seen late by Nikica Jelavic and the Croatian could only send an improvised effort over the bar with his knee.
But the visitors took the lead just before the interval when Tony Hibbert's cross hit Marc Wilson and glanced in off Crouch's back.
Everton continued to soak up Stoke's direct attacks and Jelavic, Steven Pienaar and Leon Osman combined for the latter to slice wide from a good position.
Everton unlucky not to win - Moyes
Pulis attempted to spark his team with a treble substitution and, within moments, it made a difference.
Jerome charged on to a loose ball near the halfway line and neither Phil Jagielka or John Heitinga made a challenge before the striker produced a calm finish.
The Potters striker also lifted a header over the bar from a ball shortly after before Huth had a free-kick deflected straight to Tim Howard.
Stoke manager Tony Pulis:
"We looked a little bit jaded after playing Arsenal here at the weekend. Everton are a good side but the attitude in the second half was fantastic.
"I'm no genius. If (the treble change) works, it works, and I felt it was right to put a bit of pace up the sides and up the top and the two lads did smashing and Glenn anchored the midfield well.
"QPR and Bolton are fighting for their lives and our final two matches will be a great challenge for us."
Everton manager David Moyes:
"You would expect them to finish strongly with the crowd behind them. It was a good point but we looked like scoring the second goal and played some good stuff so we are unlucky not to go away with the points.
"We're not impressed by the defending for their goal. You would hope someone would take the ball off him.
"(Finishing above Liverpool) is not desperately important, the important thing is to finish in the top 10 and this point might just about secure that. If we can win the last two games and finish up there it will be a good season for us."
Full Time The final whistle is blown by the referee.
Glenn Whelan restarts play with the free kick. Shot by Robert Huth from 25 yards. Tim Howard makes a save.
90:00 +3:54 Booking
Booking Steven Pienaar is shown a yellow card for unsporting behaviour.
Foul by Steven Pienaar on Ricardo Fuller, free kick awarded.
Inswinging corner taken by Glenn Whelan, Robert Huth takes a shot. Phil Jagielka gets a block in. Kenwyne Jones produces a right-footed shot from close in that clears the bar.
Centre by Tony Hibbert, save by Asmir Begovic.
Substitution (Everton) makes a substitution, with James McFadden coming on for Leon Osman.
Nikica Jelavic has an effort at goal from deep inside the area missing to the right of the goal.
The ball is delivered by Marouane Fellaini, Robert Huth gets a block in.
Glenn Whelan fouled by Marouane Fellaini, the ref awards a free kick. Glenn Whelan takes the free kick.
Nikica Jelavic crosses the ball, Ricardo Fuller manages to make a clearance.
Tony Hibbert delivers the ball, Marc Wilson manages to make a clearance.
Denis Stracqualursi sends in a cross, Matthew Upson makes a clearance.
Free kick taken by Ryan Shawcross.
Substitution Denis Stracqualursi on for Magaye Gueye.
Free kick awarded for an unfair challenge on Robert Huth by Nikica Jelavic.
Inswinging corner taken from the left by-line by Glenn Whelan, clearance by Sylvain Distin.
Outswinging corner taken by Magaye Gueye from the left by-line, Phil Jagielka produces a header from the edge of the box and misses to the right of the goal.
The ball is swung over by Tony Hibbert, clearance made by Robert Huth.
Free kick awarded for a foul by Cameron Jerome on Phil Jagielka. Direct free kick taken by Tim Howard.
Unfair challenge on Marc Wilson by Nikica Jelavic results in a free kick. Direct free kick taken by Matthew Upson.
Header from deep inside the penalty area by Cameron Jerome goes harmlessly over the crossbar.
Assist on the goal came from Matthew Upson.
68:21 Goal scored
Goal - Cameron Jerome - Stoke 1 - 1 Everton Goal scored by Cameron Jerome from inside the box low into the middle of the goal. Stoke 1-1 Everton.
Substitution Glenn Whelan joins the action as a substitute, replacing Rory Delap.
Substitution Cameron Jerome comes on in place of Peter Crouch.
Substitution (Stoke) makes a substitution, with Ricardo Fuller coming on for Jonathan Walters.
Marc Wilson delivers the ball.
Tim Cahill concedes a free kick for a foul on Jonathan Walters. Matthew Upson takes the free kick.
The ball is delivered by Matthew Etherington, Tim Cahill makes a clearance.
Jonathan Walters crosses the ball, Johnny Heitinga manages to make a clearance.
Free kick taken by Johnny Heitinga.
Booking Booking for Ryan Shawcross for unsporting behaviour.
Foul by Ryan Shawcross on Steven Pienaar, free kick awarded.
Marc Wilson sends in a cross, Tim Howard makes a save.
Robert Huth produces a cross.
Robert Huth fouled by Magaye Gueye, the ref awards a free kick. Direct free kick taken by Matthew Upson.
Matthew Etherington produces a cross.
Leon Osman produces a left-footed shot from the edge of the area and misses to the left of the target.
Free kick awarded for a foul by Nikica Jelavic on Jonathan Walters. Marc Wilson takes the free kick.
Leon Osman takes a shot. Save made by Asmir Begovic.
Booking Marc Wilson is shown a yellow card for unsporting behaviour.
Outswinging corner taken by Matthew Etherington, clearance made by Leon Osman.
The ball is delivered by Jonathan Walters, clearance by Phil Jagielka.
The assistant referee flags for offside against Peter Crouch. Indirect free kick taken by Tim Howard.
The ball is crossed by Matthew Etherington, Phil Jagielka makes a clearance.
Unfair challenge on Dean Whitehead by Marouane Fellaini results in a free kick. Matthew Upson crosses the ball from the free kick right-footed from right channel, clearance made by Marouane Fellaini.
Free kick awarded for an unfair challenge on Rory Delap by Marouane Fellaini. Ryan Shawcross takes the direct free kick.
The ball is swung over by Magaye Gueye, Ryan Shawcross makes a clearance.
Robert Huth fouled by Magaye Gueye, the ref awards a free kick. Matthew Upson restarts play with the free kick.
Unfair challenge on Robert Huth by Magaye Gueye results in a free kick. Asmir Begovic takes the free kick.
The referee blows his whistle to start the second half.
45:00 +2:02 Half time
Half Time The first half comes to an end.
A cross is delivered by Steven Pienaar, save by Asmir Begovic.
Free kick awarded for an unfair challenge on Peter Crouch by Marouane Fellaini. Direct free kick taken by Marc Wilson.
Assist on the goal came from Tony Hibbert.
44:00 Goal scored
Goal - Peter Crouch - Stoke 0 - 1 Everton Own goal by Peter Crouch. Stoke 0-1 Everton.
Matthew Upson gives away a free kick for an unfair challenge on Nikica Jelavic. Free kick taken by Steven Pienaar.
Headed effort on goal by Kenwyne Jones from inside the penalty box misses to the right of the goal.
Steven Pienaar takes a shot. Save made by Asmir Begovic. Outswinging corner taken left-footed by Magaye Gueye from the left by-line. Effort from the edge of the penalty box by Magaye Gueye goes wide of the right-hand upright.
Inswinging corner taken by Steven Pienaar from the left by-line played to the near post, clearance by Peter Crouch.
Corner taken by Magaye Gueye from the right by-line.
The ball is swung over by Jonathan Walters, clearance by Phil Jagielka.
The ball is swung over by Magaye Gueye, Shot from deep inside the area by Nikica Jelavic goes over the bar.
Tony Hibbert delivers the ball, Matthew Upson manages to make a clearance.
Corner taken by Matthew Etherington from the right by-line, clearance made by Tim Cahill.
Robert Huth takes a shot. Save by Tim Howard.
Leon Osman takes a shot. Save by Asmir Begovic.
Marc Wilson delivers the ball.
Leon Osman takes a shot. Save by Asmir Begovic.
Marouane Fellaini takes a shot. Blocked by Ryan Shawcross.
Free kick awarded for a foul by Marc Wilson on Tony Hibbert. Phil Jagielka takes the free kick.
Magaye Gueye delivers the ball, Robert Huth makes a clearance.
Substitution Magaye Gueye joins the action as a substitute, replacing Victor Anichebe.
Robert Huth produces a header from deep inside the six-yard box that clears the crossbar.
Free kick awarded for an unfair challenge on Kenwyne Jones by Tim Cahill. Asmir Begovic restarts play with the free kick.
The ball is sent over by Sylvain Distin.
Shot from just outside the box by Matthew Etherington goes over the bar.
The ball is crossed by Matthew Etherington, Unfair challenge on Sylvain Distin by Jonathan Walters results in a free kick. Free kick taken by Tim Howard.
The ball is crossed by Matthew Etherington, Sylvain Distin makes a clearance.
The ball is crossed by Jonathan Walters, save by Tim Howard.
Free kick awarded for an unfair challenge on Peter Crouch by Sylvain Distin. Robert Huth takes the free kick.
Corner taken right-footed by Steven Pienaar to the near post, clearance made by Ryan Shawcross.
Victor Anichebe delivers the ball, Marc Wilson makes a clearance.
Corner taken right-footed by Leon Osman from the right by-line, Headed effort from inside the area by Sylvain Distin misses to the left of the goal.
Robert Huth takes a shot. Save made by Tim Howard.
Kenwyne Jones concedes a free kick for a foul on Phil Jagielka. Tim Howard takes the direct free kick.
The game gets underway.
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