Bobby Zamora took Albion to the top of the table with a dramatic second half double.
The Seagulls' young goal king equalised from a Paul Watson free kick in the 68th minute, then clinched victory eight minutes later with a penalty after Dennis Lawrence handled from a Watson corner.
Zamora has now grabbed seven goals in nine games and he should have completed his hat-trick in injury time when the hapless Lawrence handled again from Zamora's cross.
Kristian Rogers kept out Zamora's second spot-kick, but Micky Adams' men still celebrated their first away win for seven matches stretching back to April.
It was an amazing transformation after Stephen Thomas had fired Wrexham into a deserved 66th minute lead.
Albion made three changes to the side beaten 3-0 by Southampton in the Worthington Cup at Withdean on Tuesday.
Pitcher came in for his full debut and Mayo and Hart were both recalled to the starting line-up.
Skipper Rogers, Brooker and Steele were relegated to the bench.
Wrexham made one change to the team which beat Bury 1-0 at home on Tuesday, their first win of the season.
Blackwood was preferred in midfield to Edwards, who is one of three Trinidad and Tobago internationals on the Welshmen's books.
Willy Miller, Wrexham's new signing on a three month loan deal from Dundee, was among the spectators.
Oatway took over as Albion's captain in a new 4-5-1 formation, with Pitcher joining him and Carpenter in the centre of the park and Hart and Jones on the flanks.
The players wore black arm bands and a minute's silence was observed before kick-off for the victims of the terrorist attack in America.
Mayo had his name taken in the third minute for tugging back Trundle as Wrexham's dangerman latched on to a pass from Ferguson through the middle.
Ferguson, curled the ensuing free-kick from 25 yards out around the six man defensive wall towards the top corner of the net, but Kuipers got his angles right to make a comfortable catch.
Wrexham poured forward in the early stages as rain swept across the ground.
A header by the 6ft 7in Lawrence from a Ferguson corner was kept out by Kuipers moving to his left.
Within a minute another corner from Ferguson was met by Carey with a firm header which Hart hacked off the line.
Pitcher eased the early pressure on the Seagulls with a positive run into the box to earn a corner.
Pitcher and Watson, making his 100th appearance in a row for Albion, worked the ball to Jones just outside the area, but he dragged his effort wide.
Wrexham's veteran midfielder Russell, a former Albion apprentice, collected a caution midway through the half. He sent Jones sprawling as the Seagulls' Welshman tried to make ground down the left wing from Mayo's short free-kick.
Albion were having to work hard to keep a lively Wrexham outfit at arm's length.
Trundle looked particularly troublesome and he was only narrowly wide with a left foot shot on the turn from 20 yards from Carey's pass.
Trundle, snapped up from League of Wales club Rhyl for £50,000, went close again in carbon copy fashion a few minutes later.
Albion, without an away goal since Zamora's promotion clincher at Plymouth last season, did little in the opening half hour to suggest that barren streak would end.
The pint-sized Pitcher almost ended the drought on 32 minutes with a header just wide from Mayo's right-wing cross.
Pitcher was proving quite influential and he provided a chance which Zamora really should have buried.
The former Kingstonian midfielder progressed to the byline to deliver a cross which found Zamora unmarked beyond the far post, but Albion's young hotshot side-footed tamely wide from eight yards.
Jones picked up the third yellow card of the contest with seven minutes of the half remaining for a foul on Faulconbridge.
Several Albion players appealed for a penalty when Zamora glanced a header wide from Watson's smartly taken free-kick. They felt he had been pushed by his marker Carey, but referee Laws did not agree.
Carey got himself in a terrible tangle moments later. His mistake allowed Zamora to break into the box and he went down again as Carey tried to recover and keeper Rogers advanced, but there were no claims for a penalty by the Albion players this time.
The Seagulls had come into the game much more leading up to the break as Wrexham began to concede possession too easily.
They were almost punished when Ferguson gave the ball away just outside his own box on the stroke of half time. Jones set up Oatway for a low drive which flashed just wide of the target.
The giant Lawrence headed inches over from Ferguson's corner for the home side seven minutes into the restart.
Albion had a huge let-off two minutes later, Faulconbridge putting the ball wide at the far post from point-blank range from Holmes' dangerous cross.
Albion made a double substitution on 57 minutes, Steele replacing Hart and Brooker coming on for Jones in a switch to 4-4-2.
Steele joined Zamora up front, with Brooker introduced on the right flank and Pitcher moving to the left.
Within seconds of the changes being made Kuipers dived full length to deflect Trundle's angled drive from 12 yards for a corner.
Wrexham went in front midway through the second half with a wonderful goal started and finished by Thomas. He released Faulconbridge with a crossfield pass down the right.
Trundle then pulled away outside the area to collect possession from his strike partner before threading Thomas through to score with a left foot shot from 15 yards.
It was no more than Wrexham deserved on the balance of play, but Albion to their credit took only two minutes to respond.
Watson's quickly taken free kick caught the home defence unawares and Zamora swooped to convert the Seagulls' first away goal for 11 hours and 22 minutes.
Mayo missed a glorious chance to give Albion an unlikely lead after Wicks had been cautioned. The left-back dragged his shot wide when Steele put him clean through.
The Seagulls went in front with 14 minutes left when Lawrence handled in an aerial contest with Wicks from a Watson corner and Zamora calmly sent Rogers the wrong way from the resulting penalty.
It was a remarkable turnaround and testimony to Albion's character.
Wrexham made two late substitutions, bringing on Edwards for Thomas and Morrell for Warren, while Albion introduced Rogers for Pitcher with two minutes left.
Zamora had an opportunity to complete his hat-trick when Lawrence handled his cross in the 91st minute, but his penalty was saved with his legs by keeper Rogers.
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