This was club captain Jamie's fourth reserve outing after recovering from knee surgery and he talked afterwards of pushing back into the Premiership reckoning.
His goal had more than a touch of fortune, however, as his strike from the edge of the box took a wicked bounce over visiting keeper Alan Blayney before nestling in the back of the net.
There were few complaints though and a hard-earned victory was sealed when man of the match Dean Marney finished in style from Rohan Ricketts' defence-splitting pass.
The visitors started brightly and both Agustine Delgado and Dexter Blackstock had sights at goal before OJ Mabizela's weak back header handed the chance of the half to Delgado, who nipped around Burch only to shoot into the side netting.
In-between, Blayney saved well from Lee Barnard after Marney's first notable raid down the right flank.
His next forray led to the opening goal five minutes before the break. Hughes played the ball inside the full-back, Marney sped onto it, reached the byline and clipped the perfect cross for Ricketts to nod home at the far post.
Barnard had an early headed chance at the start of the second half but the visitors stepped up a gear and deserved their equaliser after 63 minutes.
It was a decent goal as well as Jo Tessem headed Crainey's throw into Griffit's path and his low, first-time cross was tapped home by Blackstock.
Slabber, more aggressive than of late, rifled a 25-yarder just wide and Delgado looped a header over as both sides looked for the crucial third goal.
Redknapp, aided by a kind bounce, ensured it went the right way after 73 minutes. Barnard's drive was tipped aside by Blayney but from the corner, Marney picked out Redknapp on the edge of the box and the midfielder's low shot kicked up off the turf, popped over Blayney's dive and home.
Marney finished it off 10 minutes later with a delightful dink over Blayney after Ricketts' pass set him through on goal.
40mins: GOAL. Marney broke offside trap, into box, stood up perfect cross for Ricketts to nod home from close range. 1-0.
63mins: GOAL. Tessem cushioned header from throw in to Griffit, low cross tapped home by Blackstock. 1-1.
73mins: GOAL. Marney pulled corner back to Redknapp on edge of box, drove shot into the ground that took wicked bounce over Blayney. 2-1.
83mins: GOAL. Ricketts released Marney sprinting in off right wing, clipped cool finish over Blayney. 3-1.
Line-ups: Spurs: Burch, Foster, McKie, Hughes, Mabizela, Bunjevcevic, Marney, Redknapp, Barnard, Slabber, Ricketts. Subs: Forecast, Dobson, O'Hara, McKenna, Lee.
Southampton: Blayney, Kenton, Crainey, Folly, Williamson, Hall, Anaclet (Best, 80), Blackstock, Delgado, Tessem, Griffit. Subs: Anderson, McNeil, Roche, Cranie.
Jamie Redknapp completed 90 minutes for the first time since September and capped it with a goal as our reserves toppled Southampton 3-1 on Monday night.