After taking only a solitary point from their previous seven contests against the Shots, the Brewers had a gilt-edged opportunity to end the hoodoo at the Recreation Ground on Saturday.
Daryl Clare gave them the lead in 55 seconds — Albion's quickest goal in non-league's top flight — and when Andy Corbett added a second with only 14 minutes on the clock, there seemed only one possible outcome.
But the jinx lived on for another season as the Shots, aided and abetted by referee Mike Mullarkey, dragged themselves off the floor to repeat their victory at the Pirelli Stadium in December.
The Devon official controversially awarded the home side a face-saving 26th minute penalty — and it proved the turning point of a pulsating encounter.
Ryan Williams reduced the deficit from the spot and, after John Grant's equaliser, it was the diminutive midfielder's deflected 78th minute shot that denied the Brewers the consolation of even a share of the spoils from arguably their brightest away performance of the campaign.
Albion made a glut of chances, twice hitting the woodwork, but little else went right for them as the Shots rode their luck in and around both penalty areas.
Oh, and there was also the usual element of self-destruction about the Brewers as the fixture again brought out the worst in them defensively.
The penalty decision against skipper Darren Stride was unquestionably harsh, but was partially invited by Albion's failure to clear their lines.
And the home team's second and third goals were the product of poor defending that has now resulted in the Brewers conceding 22 goals in eight Conference games against the Shots.
Albion made two changes from the side that beat St Albans City 1-0 at the Pirelli Stadium.
John Brayford deputised for the suspended Gary Rowett at right-back and, more surprisingly, Shaun Harrad was preferred up front to loan signing Lloyd Opara, who was joined on the bench by new signing Marc Goodfellow.
The Shots were desperate for a change in fortunes after being humbled 3-0 by Forest Green in midweek — a result that, according to local intelligence, had left manager Terry Brown clinging to his job.
Instead, their fragile confidence took another knock when Clare struck with his 13th goal of the season.
Skipper Darren Stride's long free kick to the left corner flag was rolled back down the line by Keith Gilroy and Aaron Webster's sumptuous cross was taken on the volley and thundered home from seven yards by the Brewers' leading marksman.
Albion continued to rampage forward, Clare shooting wide from Andy Corbett's cross, and the Shots were in such disarray at the back that a second goal never seemed far away.
It came in the 14th minute courtesy of move started in his own half by Danny Holmes.
Clare's cross from the right sent panic through the home ranks and a poor attempt at a clearance by Rhys Day gave Andy Corbett the chance the slide the ball into the gaping net.
Webster might have made it 3-0 in the 22nd minute but Bull plunged to his right to clutch the full back's header after a Harrad cross from the right.
Albion looked in total command, but the Shots were thrown a lifeline when they were awarded the debatable penalty three minutes later.
The Brewers initially made hard work of making a clearance close to the touchline but after a ricochet off Gilroy, Stride appeared to catch Ryan Williams only after a genuine attempt to ease the danger.
Referee Mike Mullarkey possibly deemed that Stride's foot was too high, but the absence of protests among the Aldershot ranks suggested it was a harsh decision.
Williams convincingly beat Kevin Poole from the spot and suddenly it was a game involving two brittle defences.
Albion should have scored a third when Gilroy preyed on more indecision in the home ranks only for Harrad to sky his 12-yard shot in the 36th minute.
But instead of being two goals to the good, the Brewers found themselves back on level terms two minutes later.
Poole appeared to call for the ball as Williams crossed from the right byline, but Stride chose to make a header at the near post and only succeeded in looping the ball to opposite upright, where John Grant rose above Brayford to nod home from a yard out.
Remarkably, at the end of a half that had provided a feast of entertainment, Clare went within a whisker of putting the Brewers back in front.
In stoppage time, Harrad drilled a low cross from the right, but the ball rolled agonisingly wide of the far post from his fellow striker's clever flick.
Both teams continued to go full pelt in search of a third goal, and Albion were desperately unlucky not to get it in the 52nd minute.
Clare held off Day to glide the ball to the edge of the area, where Harrad cleverly nicked it over Marcus Gayle before crashing a 15-yard volley crash against Nikki Bull's right-hand post.
Webster had to produce a timely challenge to deny Grant on the edge of the six-yard box as both teams continued to flirt with danger, but it was Albion who again looked the more threatening team.
Harrad had a shot deflected over from 15 yards and, from Gilroy's corner kick, Webster's header was cleared a yard short of the goalline by David Lee.
The Shots were clinging on grimly again and had a further escape in the 73rd minute when another Gilroy corner brought more chaos to their penalty area.
With his back to goal, Clare improvised with a clever back-heel but was denied by a goalline clearance.
Against this backdrop of misfortune, it came as no surprise that Aldershot's winning goal in the 78th minute was a combination of all the elements that had conspired against Albion.
Holmes was guilty of indecision as a partial clearance dropped on the edge of the area, but there was also a suggestion of handball as Williams gained possession and then saw his shot beat a wrong-footed Poole with the help of a wicked deflection.
As if to confirm that luck had fully deserted the Brewers, they were denied the point their attacking endeavours deserved when Clare's 22-yard lob bounced to safety off the top of the crossbar.
With thanks to the Burton Mail.