Not surprisingly, the only other realistic chance of a breakthrough came via a Delap throw-in or home corner.
The Premier League new boys were not to be denied and Delap wound up another throw.
Delap's long-range shot tested Robert Green but it was a rare second half attack for the visitors.
Stoke took the lead at Stamford Bridge through Rory Delap's deft chip over Petr Cech after 60 minutes.
It is the second Stoke dismissal in as many games after Rory Delap's red card against Manchester City last Saturday.
The Premier League side took the lead in the 14th minute when John Carew headed in Rory Delap's long throw-in.
Sidibe was credited with the touch on Rory Delap's long throw to deny Villa, who twice battled back to level.
Predictably, both teams were at their most dangerous from set-pieces, and Stoke's second goal followed a trademark long throw from Delap.
"I'm very proud and it goes on top of what's been a very good season for us, " Delap told BBC Radio Stoke.
The visitors' change in intentions led to their first shot on goal when Rory Delap forced a smart save from the largely-redundant Pepe Reina.
Pulis cited the example of Delap's sending off last week and compared it to a similar incident involving Steven Gerrard in Liverpool's game against Chelsea.
Stoke's main attacking threats came from Pugh, Fuller's counter-attacks and inevitably Rory Delap's long throws, but neither keeper was overly tested in the first half.
Delap was fouled by Martin Laursen to allow Liam Lawrence to fire Stoke ahead from the penalty spot, with John Carew scoring a well-crafted equaliser.
There was also a prize for midfielder Rory Delap, who was voted as the player of the year by manager Tony Pulis and his coaching staff.
Stoke's first goal came courtesy of another dangerous Delap throw-in, which was flicked in by Carew past the Brezovan, who appeared to flap at the delivery.
Stoke were still keen on a winner and Delap launched another throw which saw Leon Cort land a header on the roof of the Villa net.
Fuller almost doubled Stoke's lead on the stroke of half-time when he got the better of Curtis Davies to meet another Delap howitzer throw and nodded just wide.
The Premier League new boys took every opportunity to shell the ball into the Villa box, with Delap testing out keeper Brad Friedel's resolve with his artillery-distance throws.
Pulis sent on Fuller for Rory Delap as Stoke went in search of an equaliser, while Martinez brought on Jordi Gomez for Scotland in an attempt to shore things up.
Rory Delap's ever-reliable throw-ins presented Stoke with a good chance when the Irishman's long hoist was punched unconvincingly by Cech straight to Etherington, whose goal-bound shot was blocked by Drogba.
Stoke have never won at the Stadium of Light and without the suspended Rory Delap, their chief weapon, they battled hard but offered little to suggest they would break their duck.
The Stoke boss made four changes to the side which played out an uninspiring goalless draw against Sunderland, with Andy Wilkinson, Lawrence, Rory Delap and Fuller all drafted into the starting line-up.
Stoke dug in and a trademark long throw from Rory Delap was headed towards his own goal by John O'Shea, only for Edwin van der Saar to claw the goalbound ball to safety.
Pulis went on to say he was impressed with the performance of new signing Beattie after the debutant striker, a midweek signing from Sheffield United, set up Rory Delap for the opening goal.
Sidibe tested Carson with a superb 25-yard strike after some nifty footwork and Rory Delap showed there is more to his game than an outrageous long throw when he shot over the bar after an impressive run from midfield.
He first waved away Villa appeals when Seyi Olofinjana appeared to bundle Agbonlahor to the ground, but seconds later was pointing to the spot at the other end, after Delap was clipped by Laursen as he turned tightly.
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