Albion continue to trail at the Bescot Stadium but are desperately unlucky not to draw level.
The hosts' defence lives a charmed life as three times in the space of 14 minutes the woodwork denies the Seagulls a deserved goal.
*The towering Beasant, wearing a cap as protection from the sun, was quickly in the action as he made a clean catch from Sonner's early corner.
Brooker, operating once more in a free role between the midfield and front men, ran at Hay from Zamora's lay-off.
Walsall's big central defender managed to block him out at the expense of a corner, the first of two in quick succession for Albion.
They came to nothing and the Seagulls found themselves behind after only seven minutes.
Sonner fed the overlapping Bazeley and Leitao climbed above Pethick at the far post to meet the cross with a firm downward header which gave Beasant no chance.
The only consolation for Steve Coppell's strugglers was that they were 2-0 down after seven minutes when Walsall beat them at Withdean.
Leitao, having notched his tenth of the campaign in all competitions, went looking for another when Sonner's pass released him through the inside right channel but Mayo covered.
Zamora had an opportunity to cancel out the Saddlers' embryonic advantage from a pass by Mayo, but he dragged an angled shot wide of the far post from 12 yards.
Walsall, looking threatening going forward, came close again with a drive by Sonner from outside the area which served narrowly wide of the target.
Walsall turned defence into attack in exhilarating style when Barrett attempted to control Carpenter's bouncing cross to the near post on his chest.
Hay's no-nonsense clearance was seized on by the alert Leitao on the right flank. He made ground into Albion's half and the move only broke down when his through ball, meant for Zdrilic, was intercepted by Jones.
Corica's ambitious bid to chip Beasant from 25 yards gave Albion's new No. 1 a comfortable save.
Leitao continued to give the Seagulls all sorts of problems with his pace and movement.
He got away from Mayo, despite being tugged back, before Cullip came to the rescue with a firm challenge inside the Albion area.
Albion almost fell further behind on 28 minutes. Corica's shot on the run from the brink of the box was not held by Beasant, but he redeemed himself by denying both Leitao and then Zdrilic as they tried to pounce on the loose ball.
The Seagulls forced half a dozen corners in the opening half hour without seriously threatening Walker in the Walsall goal.
There was at least some encouragement from elsewhere, with relegation rivals Sheffield Wednesday, Stoke and Grimsby also all 1-0 down by the same stage.
Brooker produced a disappointing cross from Watson's quickly taken free-kick during a period in which Albion controlled the possession.
This made the home supporters a little edgy and their anxiety increased when Barrett's flick enabled Brooker to find Zamora inside the box, he checked on to his right foot for a shot which took a deflection on its way through at comfortable speed to Walker.
Carpenter needed treatment after he was fouled 30 yards out by Corica. Pethick, set up by Oatway, struck the ensuing free-kick well wide.
Oatway was also in the wars, referee Jones halting play for the midfielder to receive treatment for a wack on the head.
Albion had done pretty well since going behind so early without finding a cutting edge to seriously trouble Walsall trio of sturdy centre halves.
Half-Time: Walsall 1 Albion 0.
Albion made a change for the second half, Rodger replacing Carpenter after his knock shortly before the break.
Jones headed well wide early into the restart of a contest the Seagulls could not afford to lose in order to maintain a realistic hope of finishing above their opponents.
Zamora was desperately unlucky not to level four minutes into the second half. He played a one-two with Brooker before lobbing the ball over the stranded Walker and on to the top of the crossbar from eight yards.
Pethick thought he had put Brooker through with a raking pass from inside his own half a couple of minutes later.
Walker had initially back-tracked but dashed off his line to reach the ball just before Brooker.
Pethick then tried to catch Walker off his line with a quick free-kick from long range, but his effort was too high.
A pass by Brooker released Barrett in behind the Walsall defence. He cut inside to shoot against the formidable figure of Hay when a cross for better placed team mates was needed.
Barrett's single-mindedness was perhaps understandable. He vowed in the run-up to the match to be more selfish in an effort to end his goal drought.
Albion were enjoying a real purple patch, with Brooker the next to come agonisingly close to an equaliser. His toe-poke from close range after Rodger put him through was turned just past the post for a corner by Roper.
Three minutes later Zamora was denied by the woodwork again in controversial circumstances.
Albion continued attacking with Roper down injured on the edge of his own area.
Brooker's cross was clawed away by Walker only as far as Zamora, whose header towards the vacant net hit the bar.
Roper was unable to continue and Emblen replaced him as part of a double substitution on the hour mark, with Carbon also introduced at the expense of Corica.
Incredibly the woodward foiled Albion for the third time in the space of 14 minutes as Rodger's left-footer from 15 yards from Watson's low centre crashed against the upright.
Having totally dominated since half time, Albion had Beasant to thank for preventing their deficit from doubling on 67 minutes.
Leitao's back heel gave Zdrilic a clear sight of goal 12 yards out. His low drive seemed destined for the far corner of the net when the diving Beasant's outstretched right hand diverted it for a corner.
Substitute Carbon collected the first caution of an increasingly eventful encounter a minute later before Albion resumed their second half superiority.
The relentless pattern of near misses continued as Watson's back-pedalling header from a left wing cross by Jones was tipped over by Walker.
The Seagulls made a substitution with 12 minutes remaining, Hart coming on upfront for Barrett who kicked the turf in frustration as his number came up.
Albion made a further change in the closing stages, Blackwell coming on for Oatway and Pethick pushing into midfield.
The late substitution almost paid off as Hart's bullet header on the stroke of full time was somehow pushed over by the acrobatic Walker.
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