The new head coach, under the watchful eye of director of football Sir Clive Woodward, saw his injury-hit side more than match promotion-chasing United until former Saint Shipperley struck 10 minutes into the second half.
Two defeats in two games for chairman Rupert Lowe's dream team sees the Saints languishing 25 points behind their latest conquerors and just nine points above the Coca-Cola Championship relegation zone.
And while fears of the drop will not be an issue, Saints' ninth manager in nearly nine years under Lowe has plenty to ponder if he is going to haul the club into the play-off places.
Burley responded to Boxing Day's 3-0 defeat at Watford by bringing in Darren Powell, Kenwyne Jones and Djamel Belmadi while dropping 16-year-old Theo Walcott to the bench.
Goalkeeper Antti Niemi was conspicuous by his absence from the squad, the club claiming the Finn has yet to recover from a virus amid speculation he is unsettled at St Mary's.
Neil Warnock, whose side sit 11 points clear in second, also made three changes with Derek Geary, Chris Armstrong and Steve Kabba all back in the starting line-up.
Burley's task on the south coast will surely be helped by the array of young talent at the club, and with Walcott under wraps it was left to 17-year-old Nathan Dyer to catch the eye in an encouraging first-half display.
One shimmy followed by a clever chip found Jones in the penalty area but the striker's touch let him down, while a neat reverse pass almost played in Brett Ormerod.
The pacy winger, who has just returned from a loan spell at Burnley, then sped past a lumbering David Unsworth but a heavy touch allowed Paddy Kenny to gather.
Unsworth was already looking like he was going to be in for a long night, and after just 19 minutes he earned a yellow card for a cynical bodycheck as Dyer was about to motor past him again.
Kenny somehow kept Saints out just before the half hour when Belmadi crossed from the left. The keeper blocked Ormerod's point-blank effort and managed to keep out Rory Delap from the rebound.
Phil Jagielka and Kabba shot wide, but the Blades came up with little else to worry stand-in keeper Paul Smith until after the break.
Shipperley was thwarted by a last-ditch challenge from 19-year-old centre-half Matthew Mills, making his home debut, but the frontman lost his marker in the 55th minute to give United the lead.
Danny Webber, on his 24th birthday, robbed Martin Cranie near the halfway line, galloped down the right flank and played a measured diagonal pass for Shipperley to slot home.
Kabba should have doubled the advantage shortly after, but wastefully shot into the side-netting.
The introduction of Walcott, just after the hour, briefly raised spirits and Jones thumped a shot narrowly wide with Kenny at full stretch.
And another sub, Dexter Blackstock, should have equalised but just failed to connect properly with his head with the goal gaping.
But the Blades saw out the final 10 minutes without being unduly troubled to take another big step on the road to the Premiership.