Albion had to settle for a point against their arch rivals and a fourth clean sheet on the trot at Withdean.
The Seagulls dominated throughout but could not find a way through even after Palace had defender Danny Granville sent off on 67 minutes for a second bookable offence.
Gary Hart and Richard Carpenter had shots saved by Alex Kolinko in the first half and Graham Barrett also chipped against the woodwork before the interval.
Albion continued to attack relentlessly once Granville was dismissed and Hart volleyed over from close range with a minute left.
Seagulls, as expected, brought in Barrett up front for his first start for six games following the return of loan signing Anthony Rougier to Reading.
Palace, making their first League visit for 15 years, had Powell, Thomson and Whelan back from their lengthy injury list.
A slick move by the Seagulls nearly produced a goal in the eighth minute.
Cullip launched it by winning a header inside his own half in typically determined manner. Brooker then freed Barrett on the left wing and Hart met his cross with a first time shot from close range which was blocked by keeper Kolinko.
Palace's Latvian custodian looked less assured a few minutes later in palming away a cross-shot from Rodger, who spent 13 seasons with the visitors.
Cullip and Beasant were involved in an altercation after Ipswich's first goal last Saturday and they were not on the same wavelength to deal with a situation on the edge of the Albion box.
Beasant was way off his line, behind the Albion captain, when Cullip headed clear as far as Butterfield 40 yards out but his ambitious attempt at finding the vacant net sailed over the bar.
Mayo, pushing forward, held the ball up well on the brink of the Palace box before finding Hart. His cross was a good one but nobody was there to capitalise on it.
It was the kind of inviting delivery you would have fancied the injured Bobby Zamora to get on the end of.
Palace threatened for the first time midway through the half. Black played a quick free-kick into Thomson and his angled shot on the run from 12 yards was pushed over the bar by the alert Beasant.
The way Barrett, Brooker and Hart were linking up was encouraging for Albion and they combined to great effect on 26 minutes.
Barrett spun inside his own half to thread a pass through to Brooker down the right flank.
Hart, stretching to reach Brooker's penetrating cross to the far post, could not keep his effort down.
Granville collected the first caution of the contest a minute later for a foul on the energetic Hart.
Rodger produced a tremendous piece of defending against his old club when Adebola muscled his way past Cullip to make progress into the Albion area. Adebola tried to find Black to his right but Rodger had tracked all the way back and turned the ball behind for a corner, allbeit a little close to the post for comfort.
Rodger almost struck at the other end with another cross-shot on the volley which bounced narrowly wide.
Whelan wasted a chance to break the deadlock for Palace when Granville slipped him in. The fit-again forward, borrowed from Middlesbrough for the rest of the season, fired wide of the far post from a tight angle eight yards out.
Brooker was proving effective for Albion once again in his floating role as Carpenter unleashed a fierce 20 yarder which was beaten away by Kolinko.
Barrett was getting through some good work as well and he was desperately unlucky not to give the Seagulls the lead five minutes from the break.
Mayo tenaciously won possession to find the Irishman through the inside right channel. His audacious chip from outside the area dipped over Kolinko and hit the upright, then Brooker headed the rebound over from close range.
Albion suffered a blow before half time as Cullip went off injured. Pethick, now fully recovered from a back injury, took the skipper's place in the centre of defence on his 50th League appearance for the club.
Kolinko had been much the busier of the two keepers and the only thing missing from Albion's bright first half performance was a goal.
Palace, relieved to still be level, introduced Borrowdale in place of the highly rated Gray for the second half.
Albion rediscovered their momentum when Barrett put Brooker in behind the Palace defence for a low cross which just eluded Mayo.
The marauding Brooker was having a fine match. His next contribution was to put Barrett through one-on-one with Symons, but his shot from just outside the area drifted wide.
The match took a dramatic turn when Palace were reduced to ten men with 23 minutes remaining. Granville made a reckless challenge on Hart close to the corner flag and referee Paul Durkin sent the defender off for a second bookable offence after consulting his linesman.
The Seagulls almost made their numerical supremacy count immediately. Rodger's resulting free-kick was cleared as far as stand-in skipper Carpenter, whose well struck volley forced Kolinko into a diving stop by the foot of his post.
Palace made a final change on 77 minutes, Antwi coming for Black as Albion continued pursue the goal their superiority warranted.
Hart spurned a great chance to snatch the points on 89 minutes, volleying over from eight yards from Carpenter's dink into the danger zone.
Albion (3-4-1-2): Beasant (gk) 7; Watson (rbw) 7, Mayo (lbw) 8, Cullip (cd) 7, Blackwell (cd) 7, Ingimarsson (cd) 7, Rodger (m) 7, Carpenter (m) 7, Brooker (m/f) 7, Hart (f) 7, Barrett (f) 7. Subs: Pethick for Cullip (injured, 43), Oatway, Jones, Wilkinson, Packham.
Bookings: None.
Crystal Palace (3-5-2): Kolinko; Granville, Butterfield, Symons, Derry, Gray, Thomson, Black, Adebola, Powell, Whelan. Subs: Borrowdale for Gray (injured, 46), Williams for Adebola (injured, 66), Antwi for Black (withdrawn, 77), Routledge, Berthelin.
Sent off: Granville (27, foul and 67, foul).
Bookings: Whelan (83, foul).
Attendance: 6,786.
Fan's View: Clare Oxley (Worthing).
What a match! The best goalless draw I've ever seen.
Albion played very well but didn't have the bit in front of goal. If only Bobby had been playing, he surely would have got a hatful.
Let's hope things work out for us and we beat them next season.
As for this evening, everyone worked tirelessly, you wouldn't have thought that after the performance at Selhurst six months ago.
On a sad note it was a shame to see violence outside the ground afterwards but letting both sets of fans out together was frankly suicide.
A lively night both on and unfortunately off the field.
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