City booked their place in round four after coming from behind to defeat Conference high fliers York.
Manager Tony Pulis fielded a suprisingly strong XI with just three changes as Tuncay, Faye and Shawcross dropped out for Fuller, Collins and Cort. Incidentily it was Cort's 50th start for the Potters. Another milestone was achieved by Liam Lawrence as the right winger notched up his 100th start for City.
The hosts started brightly and Delap had a whole host of throw ins cleared, one way or another, in the opening exchanges as panic set in when the Irishman hurled the ball into the box.
The first chance from open play arrived on six minutes as Lawrence slipped Fuller through before racing into the box to collect the Jamaican's return pass after he tricked his way past two defenders. Lawrence shot at goal but was denied by a diving defender who blocked his effort.
The visitors seemed to settle down after that opening burst and Rankine drove an effort wide before the non-leaguers won a couple of corners themselves but the City rearguard held firm.
Fuller and Beattie then went close as the Potters gained control again before a shock blow as a floated free kick struck York midfielder Neil Barrett on the back of the head and flew into the Potters net off the inside of the post. The Conference sides support went wild as they sensed another cup shock.
Those thoughts were quickly put to bed though as, sixty seconds later, Delap's missile like throw in was sliced into his own net by captain Parslow and then, in a complete turn around just a minute later, another Delap throw in produced a spot of head tennis in the York area before Fuller rose and nodded past ex-Potters loanee Michael Ingham in the York goal.
The game settled down after that spurt as the Potters had the lead they were expected to have and just saw things through to half time. The break allowed the Potters to make a change as Thomas Sorenson was replaced as a precaution after picking up a minor finger injury in the first half. His replacement, Steve Simonsen, was immediately called into action but saved well from the lively Brodie.
City were looking to wrap up the game and Huth and Cort both went close from set pieces before the hour mark before winger Matthew Etherington produced a fantastic 25 yard free kick, right in the top corner, to double the advantage.
The game petered out somewhat as a trio of subs from the home side meant the rhythm never came back and the Potters turned their attentions, with this gajme wrapped up, to Tuesdays vital Premier League encounter againbst Fulham with just Tuncay, from the edge of the box, going close late on.