Kuipers was cleared to play after having his red card in the previous home match against Bradford reduced to a yellow on appeal.
The big Dutch No 1 was forced into an early save by a stray back pass by the recalled Adam Hinshelwood.
A free-kick by Rodger from the right wing was headed away by the Derby defence as far as Carpenter, whose well struck drive from 25 yards rose narrowly over the bar.
The visitors had half-hearted appeals for a penalty rejected when Bolder went down inside the box.
Kinkladze provided a couple of early warnings for Albion. Derby's enigmatic Georgian got the better of Hart following a corner to float in a dangerous cross before Watson eventually cleared on his 150th League appearance for the Seagulls.
Kinkladze then broke down the right flank, with Mayo stranded upfield, but he wasted the opening with a disappointing cross after exchanging passes with Bolder.
Sidwell was showing up well, closing down the opposition at every opportunity. A foul on Albion's flame-haired newcomer near the halfway line led to the first caution of the contest for Elliott.
A clear push in the back by Zamora's England Under 21 team mate Riggott on Cullip gave Albion a free-kick just outside the Derby area.
Carpenter's resulting effort, struck with considerable venom, was blocked by the busy Lee.
Derby were employing the same system as the Seagulls and both back fives were generally in command in the first 20 minutes.
A fluent move by the visitors, involving several players, finished with Christie hooking a shot goalwards from 12 yards which was blocked by Mayo.
Burton created just enough room for himself inside the area to drag a shot well wide of Kuipers' left hand post as the Rams enjoyed a period of possession.
Albion survived a scare midway through the half when Christie delivered a low centre from Barton's slide rule pass.
Kuipers came out feet first to the edge of his six yard box to put off Burton as neither of them connected with the ball.
Albion were finding it difficult to fashion much going forward against a sturdy Derby rearguard operating an efficient offside trap.
Kuipers was a little indecisive as Cullip waited for him to collect from Burton's chest pass into the path of Bolder.
Bolder almost got a foot in ahead of the Seagulls custodian.
Goalmouth action was in short supply, with the teams more or less cancelling each other out.
The crowd were roused on 32 minutes as a raking crossfield pass by Barton from Kinkladze's pass was controlled by Christie.
Kuipers looked to have the edge as he rushed off his line to meet the advancing Derby forward. They reached the ball at virtually the same time and ended up in a heap requiring treatment.
Albion fans clearly felt Christie's challenge was late and they booed when he was given a yellow card rather than red.
Kuipers was okay to continue and so too was Christie.
Albion's first corner of the match shortly after, swung in by Rodger, was cleared with some difficulty by the Derby defence.
The incident involving Kuipers and Christie had galvanised the Albion fans and their team had a goal controversially disallowed five minutes from the break.
Grant, challenged by Cullip, failed to deal with Watson's free-kick from the right flank.
Hinshelwood tried to get on the end of the loose ball before it was turned in by Mayo, only for his rare effort to be ruled out by a linesman's flag.
It was hard to tell whether it was for offside or a foul, but either way it was unfortunate for Mayo as it would have taken his career tally into double figures.
Albion had to reshuffle two minutes later as Hinshelwood was forced off with what appeared to be a shoulder injury.
Jones, returning from knee ligament damage, took up his favoured left-back berth, with Mayo switching to the centre of defence.
Almost immediately Mayo misplaced a square pass to Burton just inside Albion territory, but Lee eventually fired over from Christie's layback.
Half-Time: Albion 0 Derby 0.
Albion were handed a numerical advantage six minutes into the restart as Christie was sent off for a second bookable offence.
Watson rolled the ball forward to where he thought a free-kick should be taken for the Seagulls.
Christie rather stupidly kicked the ball gently back and out of play.
Referee Beeby deemed the offence worthy of a second caution for the crestfallen Derby striker.
Albion's free-kick was then advanced ten yards by the Northampton official and Watson almost added insult to the visitors' injury when his effort deflected narrowly wide of the far post.
Burton had his name taken on the advice of a linesman on 54 minutes after an aerial challenge for a bouncing ball with Kuipers.
The Seagulls were almost punished for a lack of concentration two minutes later, Elliott miskicking from close range from Barton's corner.
Barton the former Newcastle and England defender, was replaced by Jackson on 58 minutes as Derby tried to cope with having only ten men.
Sidwell's promising first appearance at Withdean was marred by a 64th minute caution for a foul on Evatt five yards inside Derby territory.
The initiative was now very much with Albion, but Carpenter uncharacteristically lost his range with both a free-kick and a cross well over the bar.
Burton was now foraging alone upfront for Derby, but Boertien was pushing forward in the left wingback role to nullify Watson.
The Seagulls were still finding it difficult to find a way through well drilled opponents, even with an extra man.
Pethick, making his first home appearance for two months fired wide at the end of a forward thrust.
The crowd were becoming slightly frustrated, but the Seagulls were entitled to be satisfied taking into account the loss of Barrett, Blackwell and his replacement Hinshelwood.
There was more perspiration than inspiration. Zamora is always dangerous though and a moment of class from Albion's goal king almost produced a breakthrough with 14 minutes left.
His fine cross from Carpenter's slightly overhit pass was headed just wide of his own net by Riggott at the far post under pressure from Hart.
Sidwell spurned a chance to become an instant hero on 84 minutes, blazing over the rebound from 12 yards after Hart's cross had hit the bar.
Sidwell's miss did not matter as Mayo came up trumps with a minute left.
His header following a corner was blocked on the line, but the long serving defender rammed in the rebound, much to the disgust of the sheepish Rams.
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