Chris Greenacre's late strike condemned Albion to defeat in a tense basement battle.
The former Mansfield marksman swept in a low cross from lively second-half sub Lewis Neal on 83 minutes.
It was hard on the Albion defence and veteran keeper Dave Beasant.
They looked solid throughout and Anthony Rougier missed two good chances with headers at the start of each half.
Bobby Zamora returned at the expense of Graham Barrett in the only change to the Albion team beaten 3-0 at Gillingham on Saturday. Barrett dropped to the bench, where Shaun Wilkinson was preferred to John Piercy.
Stoke were unchanged following their 1-0 home defeat against Burnley on Saturday.
A bumper crowd, with prices slashed to a £5 for home and away supporters, saw the Seagulls make most of the early running.
They forced a couple of corners and Rougier, who used to play for Stoke's arch enemies Port Vale, should have given them a fourth minute lead.
The on-loan Reading front-man headed narrowly wide six yards out from Richard Carpenter's right wing cross.
Thomas, Stoke's raiding rightback, wasted a couple of crossing opportunities. The first sailed behind the goal and the second straight into the arms of Beasant as the home side struggled to settle down.
The tension was evident both on the pitch and in the stands, with no discernible pattern developing in the opening quarter-of-an-hour.
Hall's centre gave Beasant another comfortable catch after O'Connor took a quick free kick, conceded by Ivar Ingimarsson.
Thomas was off the field for treatment when former Dutch International Hoekstra received the first caution of the contest for a foul on Watson midway inside Stoke territory.
Stoke have let in a number of goals from set pieces this season and Albion should have punished them for some slack marking in the 21st minute.
Danny Cullip made an unguarded run from Simon Rodger's corner but headed well wide of the target.
Albion were looking very comfortable at the back as Hoekstra and Gudjonsson switched wings to try and inject some spark into Stoke's play.
Beasant and Cullip exchanged words before the first of two corners in quick succession for the home team. The second of them, taken by Gudjonsson, was eventually fisted clear by Beasant as far as O'Connor, whose low drive from 25 yards flashed just wide.
The exchanges were particularly frantic and untidy, with both teams frightened of making a mistake.
Rodger was booked for halting the progress of Thomas ten yards outside the right hand edge of the Albion area. Hoekstra's ensuing free kick was well claimed by Beasant.
Albion broke smartly through Paul Brooker following an important challenge inside his own box by Blackwell. Zamora then fed Rodger, supporting to his left, but his low drive was blocked by Handyside.
Rougier put the ball in the net from close range at the far post after clever approach work and a cross by Zamora, but the linesman was already flagging for offside.
It was the last meaningful action of a poor half in which Albion had the better of a paucity of chances.
Stoke made two substitutions for the second half, the injured Thomas was replaced by Richardson, on loan from Leeds, and Neil took over from Hoekstra on the left side of midfield.
Greenacre had the first on-target effort of the match a minute into the restart, an ambitious shot straight at Beasant from 30 yards after an aerial error by Cullip.
O'Connor had his name taken for clipping the heels of Zamora as he broke into Stoke territory.
Carpenter curled the ensuing free kick from 35 yards straight at Banks.
Substitute Richardson brought the home fans delight with a promising solo run which he ended with a low shot wide of the target from 20 yards.
Rougier had another chance for Albion on 53 minutes. Zamora picked out his run with a perfect cross, but Rougier lost his bearings as he back-headed well wide of the net.
A rare burst of pressure from Stoke culminated in Neal cutting inside a couple of challenges inside the Albion area before shooting meekly at Beasant.
Substitutes Neal and Richardson had brought more urgency to Stoke's play in wide areas, Beasant just managing to palm away a dangerous cross from the former.
Stoke made a third substitution with 17 minutes left, top-scorer Iwelumo coming on up front for Lee Mills. Stoke were having much more of the possession in the second half without really threatening to break through, as Albion held firm at the back.
Greenacre fired over on the turn from 16 yards before making the breakthrough which Stoke craved and Albion feared seven minutes from time.
Gunnarsson made ground through the middle to release Neal and his low cross was slotted in by Greenacre.
Albion responded by throwing caution to the wind, introducing Barrett for Watson.
Albion (3-4-1-2): Beasant (gk) 8, Watson (rwb) 6, Mayo (lwb) 6, Cullip (cd) 8, Blackwell (cd) 9, Brooker (m) 6, Carpenter (m) 7, Ingimarsson (cd) 8, Zamora (f) 7, Rodger (m) 7, Rougier (f) 6. Subs: Barrett for Watson (withdrawn 85), Oatway for Carpenter (withdrawn 88), Jones, Wilkinson, Packham.
Bookings: Rodger (31) foul.
Stoke City (4-4-2): Banks, Thomas, Handyside, Shtaniuk, Gunnarsson, Gudjonsson, Mills, Greenacre, Hoekstra, O'Connor, Hall. Subs: Richardson for Thomas (injured) 46, Neal for Hoekstra (injured) 46, Iwelumo for Mills (withdrawn) 73, Viander, Cooke.
Scorer: Greenacre (83).
Bookings: Hoekstra (20) foul, O'Connor (50) foul.
Half-Time: Stoke 0 Albion 0.
Attendance: 21,023.
Fan's View: Gary Thomsett (Brighton).
I think Steve Coppell has done wonders for us but he has to take some of the blame for this result.
I felt we lost our way totally compared to recent home and away performances in our good little run.
We went to Stoke for the draw which was totally the wrong thing to do. You could see it wasn't working. I like Rodger, he has played well for us, but I didn't think he was in the game last night.
Zamora didn't do anything, which was very noticeable, and Rougier looked unfit. We are playing long, high balls with him up there instead of keeping the ball on the ground, which we have been doing.
It was crying out to bring on Jones and Barrett and work their back four. In the end, Stoke got the goal but you could see it was going to happen. Very disappointing.
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