A bumper crowd included 1,300 Seagulls supporters on the terrace behind the goal defended by Gillingham in the first half and, rather bizarrely, 19 Dutch referees.
There was a late change of referee, Peter Walton from Northampton taking over from Berkshire's Paul Armstrong, whose wife had gone into labour.
Albion's new forward partnership demonstrated promising early understanding.
Barrett flicked a header on for Rougier, escaping between two defenders. His low cross was cleared unceremoniously into touch by Edge.
At the other end Shaw exchanged passes with Wallace to deliver a low cross which Mayo punted away from danger.
Beasant, 44 later this month, had to come smartly off his line to smother Wallace as he tried to latch on to Sidibe's header.
Rougier had the first shot on goal, a rather tame effort straight at Welsh under 21 keeper Brown after Barrett set him up.
Gillingham were looking threatening going forward and Blackwell had to be strong in the tackle to thwart Sidibe inside the box.
Beasant came to Albion's rescue in the ninth minute. Shaw threaded a pass through to Nosworthy, advancing through the inside right channel, and his low angled drive was deflected for a corner by the diving veteran.
Albion responded with an opportunity of their own a minute later, emanating from a firm challenge by Ingimarsson.
The ball broke for Brooker just outside the Gillingham area, but he screwed a right foot shot wide with Rougier unmarked ten yards out.
Albion were looking inventive themselves upfront. Brooker should have put them ahead on the quarter hour mark, with Gillingham down to ten men while Sidibe received treatment.
Rougier put the former Fulham winger through, but he missed the target from the angle of the six-yard box as Brown came to meet him.
Sidibe was unable to continue and Tommy Johnson took his place after Ashby had been penalised for a challenge on Rougier.
Watson's resulting free kick from 20 yards was saved by Brown, moving smartly across his line.
Johnson, once of Derby and Celtic, curled narrowly over the crossbar from 20 yards following an interception by Watson inside his own area.
Johnson is better remembered by Albion fans as one of Knotts County's scorers in their play-off final defeat at Wembley in 1991.
There was a pleasing ebb and flow to the contest, despite the difficult pitch conditions.
Nosworthy was proving a dangerous attacking outlet for the home side, while Rougier was doing a pretty decent job as Zamora's deputy.
Rougier's muscular but legitimate challenge on Brown as the pair converged on a hopeful ball from Cullip into the Gillingham area left the young keeper in need of treatment.
He was able to continue, but it was another example of how Rougier can use his physical attributes to unsettle defences.
Carpenter and Saunders were next to require attention from the respective physios after an accidental clash of heads as the exchanges became rather scrappier.
Rougier, fed again by Barrett, saw his low drive blocked in a heavily populated box.
Albion were giving the Gillingham back four plenty to think about. Brown had to come smartly off his line to smother at the feet of Brooker after Rougier headed on Beasant's long clearance.
Barrett fired well over the bar on the turn from 20 yards, but at least it was an attempt on goal by the shot-shy Arsenal front man, who was otherwise getting through some good work once more.
So too were the central defensive trio of Cullip, Blackwell and Ingimarsson, fresh from consecutive clean sheets.
They were exhibiting commendable discipline and resolution.
Gillingham, deprived of Sidibe's aerial presence, had lost much of their attacking zip as half time approached.
Southall's corner, Gillingham's second of the game, was headed away by the dependable Blackwell as Gillingham enjoyed a brief burst of pressure.
There was another injury worry for the home side in the dying stages of the half, stand-in skipper Smith pulling up clutching a hamstring as he tracked back to marshal Brooker.
Smith started the second half after testing his injury during the interval.
The Seagulls fell behind less than a minute into the restart after fatally losing concentration at the back.
Johnson's angled shot from 15 yards was parried by the diving Beasant, but Shaw nodded in the loose ball at the far post from point blank range.
Beasant was furious with his defenders as Shaw joined Wallace on eight League goals.
Brooker ended a promising burst into the Gillingham box with another shot off target, his finishing again letting him down.
Rougier almost levelled in crazy circumstances on 54 minutes when Smith left a back pass short for Brown.
Albion's new marksman challenged the keeper for possession 25 yards out and the ball then broke for him to have a shot which Hope blocked as the recovering Brown slipped.
Albion's impressive response to their deficit continued, Barrett cleverly making room for himself on the edge of the area to chip just over the bar as Brown back-pedalled.
Shortly afterwards Barrett headed over at the near post from Watson's inswinging cross.
The Seagulls' deficit doubled on 59 minutes via a penalty rather harshly awarded against Ingimarsson.
Johnson, latching on to Shaw's short pass, went down rather easily from the grounded Ingimarsson's tackle.
It was, in another sense, a clever piece of play by an experienced forward and Johnson stepped up to send Beasant the wrong way from the resulting spot kick.
Johnson almost struck again four minutes later, Beasant palming his lob for a corner as he stole in behind the Albion defence from Edge's ball into the box.
Albion's first-half composure had well and truly deserted them.
They almost conceded a third in freak fashion, Carpenter crashing a low cross from Wallace against teammate Ingimarsson.
It ricocheted towards goal for Beasant to make a reflex stop which he probably did not know much about.
The Seagulls made a substitution midway through the second half, Jones coming on for Mayo at left wingback.
Ashby collected the first yellow card of the match a couple of minutes later for holding back Rougier midway inside Gillingham territory.
Blackwell miskicked ten yards out amid chaotic Gillingham defending, then Rodger had a shot from the brink of the box pushed for a corner by the diving Brown as Albion hunted for a way back.
Southall stretched Gillingham's lead 14 minutes from time with a shot which took a wicked deflection off Blackwell past the wrong-footed Beasant.
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