Redknapp was a member of the mighty West Ham side, featuring three World Cup winners, which crashed out of the FA Cup at Field Mill 3-0 back in 1969.
Despite that memory he decided to rest his first-team stars, naming a completely different starting XI to the side which drew at Derby in the Championship 48 hours earlier.
But he paid the penalty as his young guns were toppled by the side third from bottom at the foot of League Two, who claimed their second Championship scalp of the season.
Giles Coke was Mansfield's hero, racing clear onto Simon Brown's incisive 68th minute pass and sliding his finish past hesitant keeper Paul Smith, who wrongly decided to stay on his goal-line.
Thirteen minutes from time Smith redeemed himself to deny Fraser McLachlan a second goal after more good work by Brown, but the Saints still slipped to only their second defeat of the season.
Southampton's young strikers, eager to impress Redknapp, had posed all the early threats on the breakaway. In the second minute Kenwyne Jones' close-range shot was saved by Kevin Pressman and a minute later Dexter Blackstock fired wide.
The best Saints chance came in the 33rd minute when a fine run and cross by Nathan Dyer created a clear opportunity for Blackstock, but his fierce, point-blank header was superbly punched to safety by Pressman.
Stags caretaker boss Peter Shirtliff, in charge for the first time after Carlton Palmer's resignation just three days earlier, gave Welsh Under-21 international striker Adam Birchall his first start as a forward at Field Mill.
And just before half-time the switch almost paid dividends, Birchall's fierce drive after a fine solo run tipped over by Smith.
Three minutes into the second half Richie Barker and Brown just failed to touch in a fine Gareth Jelleyman cross as the Stags again troubled the visitors. Then Barker, McLachlan and Coke all went close to a breakthrough for the home side.
At the other end Rory Delap similarly failed to get the vital touch as the Saints looked certain to score – and that miss proved decisive when Coke struck the winner.