Salif Diao's inclusion in the starting line up raised eyebrows but the Potters were more than a match for the hosts and fully deserved the point.
It looked as though they may have been on for all three, for what would have been only an eighth Goodison Park win in 56 attempts,after Robert Huth gave them the lead early in the second half only for Leon Osman to equalise minutes later.
City had the first attempt of the match, in the third minute, as Fuller danced down the wing before laying the ball to Etherington,. The wingers cross in was met by Beattie but his header was straight at Howard.
Everton were having the majority of the possession, Saha spun Shawcross but shot harmlessly wide and Cahill got free in the 6 yard bix but headed straight at Sorenson. Stoke were still looking dangerous though, breaking with the impressive pace of Fuller and Etherington to keep the hosts on their toes.
City had another chance shorly after when the unlikely source of Abdoulaye Faye crossed in for Fuller to nod towards goal. The effort lacked any pace though and Howard easily collected.
The ref wasn't adhering himself to the Potters fans and bookings for Fuller and Diao were both questionable as both seemed to take all the ball and little, if any, of the man. Another controversial moment arose towards the end of the half as Baines clearly used both hands to shove Delap as the midfielder rose in the box to get his head on a cross. The ref waved away the appeals, whilst Osman forced Sorenson into a brilliant save at the other end, the scousers shot flying towards the top corner.
The second half started brightly with each team striking in the opening exchanges. Firstly the Potters took the lead when an Etherington corner saw Huth rise above Cahill and direct his header towards the far corner, leaving Howard with no chance as the German opened his account for the Potters.
The hosts then drew level five minutes later when, following neat play around the City box, Osman unleashed a powerful effort that curled over Sorenson and dropped in off the underside of the crossbar. It was a fantastic strike and one which the otherwise exceptional Sorenson had no chance with.
Everton pressed for a winner and Cahill headed straight at Sorenson before Rodwell well hit effort was well saved by the City stopper.
Both sides made substitutions to try and grab a winner and he game flowed from end to end in the latter stages, Fuller, Huth and Delap all went close for Stoke whilst Baines and Yakubu both wasted good opportunities for the Toffee's whilst Jo should have scored a late winner but the ball got stuck under his feet and this allowed the defence to clear.
Stoke: Sorenson, Huth, A.D.Faye, Shawcross, Collins, Delap, Diao(Whelan 76), Whitehead, Etherington, Beattie, Fuller(Kitson 90)