Tony Pulis' men certainly reacted well to their seven-goal mauling at Stamford Bridge and Dean Whitehead soon received a lecture from referee Howard Webb for a crunching tackle on Mikel Arteta.
Stoke City 0-0 Everton: As it happened
But Everton were also up for a battle and Victor Anichebe warmed Asmir Begovic's fingers with a fierce shot as both sides wrestled for supremacy.
Ricardo Fuller scorned City's first real opportunity when he flicked a tame effort straight at Tim Howard from Mamady Sidibe's header.
And Arteta was fortunate to get away with an untidy challenge on Glenn Whelan in the penalty area as Stoke attempted to turn the screw.
Despite high levels of endeavour, a lack of real quality in the final third was a problem for both sides as defences held firm.
But Everton did threaten as half time approached when a fierce shot from Leighton Baines looked set for the top corner of the net until it was blocked by Ryan Shawcross.
Stoke made a strong start to the second half and only Rory Delap will know how he failed to give his team the lead after a terrific move in the 48th minute.
Mamady Sidibe freed Matthew Etherington and the winger's precise pass left Delap with only Howard to beat from seven yards.
The midfielder looked certain to score, but screwed his shot a foot wide with Howard motionless.
At least the miss got the Stoke fans going and the Everton rearguard started to come under increasing pressure, most notably from a string of long throws by Delap.
Whelan had one shot blocked by the defensive wall after Fuller was tripped 20 yards out and another which flashed a couple of yards wide.
But Everton were lifted by a double substitution in the 72nd minute when Louis Saha and Leon Osman were replaced by Yakubu and Jack Rodwell.
And the visitors thought they had taken the lead two minutes later when Rodwell's shot was blocked for a corner.
Arteta's far-post delivery was headed home at the far post by Phil Jagielka, but the linesman flagged that Anichebe had strayed into an offside position.
Stoke responded with Fuller twice going close towards the end, but a point apiece was probably a fair outcome.
Source: DSG
