A controversial sending off and penalty were the main talking points as the League Two side were stifled by their more experienced Premier League opposition
Jon Walters opened the scoring from the penalty spot in the first half after Rory Delap had been shown a red card for a dangerous tackle, and Peter Crouch made it two just after half-time to dash any hopes of a cup upset.
The hosts started the game brightly, winning plenty of corners in the opening stages, and almost had a dream start when the ball rebounded off Crouch and onto the crossbar seven minutes in.
Walters then had the first opportunity for Stoke in the 11th minute, flashing a shot across the face of Gilmartin's goal. The game's first real flash point came in the 17th minute as Rory Delap was sent off for a tackle on the right-back David Hunt.
The decision was a debatable one as Delap went in studs up and caught the defender, but it didn't seem to rile the Crawley players too much.
Manager Steve Evans, however, was straight out of his technical area to remonstrate with the referee, who agreed that a poor tackle had been made and showed Delap the red card.
Despite the numerical disadvantage, for the next 10 minutes it was Stoke who pressed, with an aerial bombardment at the Crawley goal.
However, the hosts held firm and Kyle McFadzean was the next to come close, hitting a long range drive that Asmir Begovic stopped easily, before Jerome dragged a shot wide when he should have done better.
But with a little under five minutes until half-time referee Mike Jones was involved again, giving Stoke a penalty for McFadzean's challenge on Ryan Shawcross. It appeared a fairly soft penalty, but there were no real complaints from the Crawley players, and Walters stepped up to smash into into the bottom corner.
And as the halftime whistle blew the referee left to a chorus of boos from both the home and away fans, but Stoke were undoubtedly in pole position despite their early red card.
The second half started poorly for Crawley, conceding a second goal within the first 10 minutes.
Claude Davis was booked for a poor tackle on Jerome after dawdling, and from Glenn Whelan's resulting free-kick Crouch looped a header in at the far post.
It was then almost three just before the hour mark as Whelan fired in another corner that just evaded Walters and Crouch at the far post. Crawley came close shortly after when Howell's cross was flicked on towards Scott Neilson at the far post, but the ball was well cleared after Neilson's pull-back.
Tyrone Barnett then came close, but his shot was blocked well by Danny Collins, who made another good block seconds later on Josh Simpson's cross.
Howell then had a clever free-kick stopped fairly easily by Begovic, as he forced his effort underneath the jumping Stoke wall.
Sanchez Watt, on loan from Arsenal, was next to come close for the hosts as he had an effort from 25 yards that flew a couple of feet over the bar, and had another shot well stopped by Begovic after a storming run by Neilson.
With time running out, it was all Crawley, boasting 82 percent of possession at one stage, but it didn't seem to be able to find a way past the resolute Stoke defense.
A very late overhead kick was as close as Crawley came, but Barnett's effort was blocked on the line by Collins, seemingly with his arm. The hosts had little to complain about however as the Potters comfortably booked their place in the next round.
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