The winger drilled a 30-yard free-kick into the bottom left corner of the net and that was enough to see off a spirited Shrimpers side, who played 79 minutes with a numerical disadvantage after John Spicer was sent off for a poorly timed tackle on former Southend striker Matt Paterson.
But Paul Sturrock's side initially remained on top with Freddy Eastwood having a deflected shot kept out by Burton goalkeeper Stuart Tomlinson in the 33rd minute.
Shrimpers winger David Martin then fired over from the edge of the penalty area after collecting a right-wing cross from Sean Clohessy.
After the break, Britt Assombalonga and Kevan Hurst sent close range headers wide of the left post from close range for the home side before Burton began to get into the game more.
As a result, substitute striker Adi Yussuff twice came close to netting a late winner for Albion before Maghoma's injury-time effort won all three points.