Sonny Bradley's 87th-minute effort handed the Shots an unlikely victory, but they were well worthy of the three points.
Dean Holdsworth's side went in front inside the first minute when Danny Hylton jinked his way past a statuesque Southend defence before firing into the bottom left-hand corner of the net from 12 yards.
Shots remained on top with Peter Vincenti wasting two good chances to score before the Shrimpers equalised in the 68th minute when Mark Phillips headed home a left wing cross from Kevan Hurst.
Southend then wasted a golden chance to score 12 minutes later when substitute Freddy Eastwood failed to convert a penalty. The spot-kick was awarded after Britt Assombalonga had been brought down by Anthony Tonkin, but Eastwood's effort was saved low down to his right hand side by Aldershot keeper Jamie Young.
The visitors then made the most of the let-off in the 87th minute when Bradley headed home after Michael Rankine's initial effort from Danny Rose's right-wing corner had been cleared off the line by Sean Clohessy.