Shipperley's goal on 55 minutes came after young defender Martin Cranie was robbed by the impressive Danny Webber who slid the ball into the six-yard area for the former Saint to finish past the indecisive Paul Smith.
Southampton began the game with eight first team members absent through injury and illness.
However, they could have taken the lead on the half hour mark when Brett Ormerod and Rory Delap were denied by an outstanding double save by Sheffield United keeper Paddy Kenny.
Kenwyne Jones almost broke the deadlock on 49 minutes when he seemed to almost move in slow motion past the static United midfield only to scuff his shot wide.
Burley's side then had two penalty appeals turned down just minutes later when both Delap and then Jones fell inside the area but referee Paul Crossley waved their half-hearted appeals away.
The impressive Webber provided much of United's attacking play and it was no surprise that he was the architect for Shipperley's goal on 55 minutes.
It was especially harsh on youngster Cranie who up until then had enjoyed a decent game.
Phil Jagielka bossed the game from midfield by playing Saints' own dynamo Nigel Quashie off the park.
His back heel to Steve Kabba nearly doubled the Blades' lead but the former Crystal Palace man screwed his shot horribly wide.
Jones tried in vain to claw one back but he could do little as his cross five minutes from time was somehow headed wide by substitute Dexter Blackstock from just two yards out.
Southampton's goalscoring problems proved alarming on this display as even the introduction of Premiership-bound 16-year-old Theo Walcott proved fruitless.