Albion's run of five straight home wins came to an end in a dour deadlock.
Lowly Wrexham became the first side to stop the Seagulls from scoring at Withdean for 13 months.
Peter Taylor's promotion chasers sorely missed goal king Bobby Zamora, who was starting a three-match ban.
That was no reflection on teenager Chris McPhee, given his full League debut as Zamora's stand-in.
The 18-year-old from Eastbourne worked hard upfront, but he lacked support against a disciplined Wrexham defence.
A subdued crowd of 6,649 saw Wrexham come closest to scoring in an uneventful first half.
Michel Kuipers acrobatically tipped over a free-kick from long range by Alex Ferguson's son Darren.
Kuipers had a let off a few minutes later when he failed to control a back pass from Robbie Pethick.
The big Dutchman had to dive on the ball to prevent it rolling into the empty net and Ferguson's resulting free-kick from the edge of the six yard box was charged down.
Albion had their best spell immediately after the break.
Their clearest chance fell to Paul Watson, but he fired over from the rebound when Wrexham's Norwegian goalkeeper Marius Rovde failed to hold a Richard Carpenter shot.
Albion, with Zamora's fellow forward Daniel Webb also beginning a two-match ban, suffered an injury blow in the first half. Gary Hart was forced off and taken to hospital as a precaution.
David Lee came on for his debut for the club and Lee Steele was brought on in place of Steve Melton midway through the second half to lend more support to McPhee.
It was all to no avail as Wrexham picked up a precious point in their fight against relegation.
Albion headed off tonight for a break in Bournemouth to prepare for Tuesday's South Coast Derby at Dean Court.
Elsewhere Reading's 1-0 win at home to Stoke took them five points clear of Albion at the top from a match more.
Brentford moved into third, six points behind the Seagulls, with a 2-1 win at home to Notts County.
Bristol City were held to a goalless draw at Colchester, while Huddersfield won 2-1 at Blackpool.
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