The midfielder struck with 14 minutes remaining after fellow substitute James Ward-Prowse provided the ammunition to cancel out Phil Bardsley's opener, and in the process left the home side still looking over their shoulders.
A point will still prove enough if Wigan lose at Arsenal on Tuesday evening for Paolo Di Canio's men and only a heavy defeat on the final day coupled with other results going against them will see Mauricio Pochettino's side go down.
Southampton started confidently and skipper Rickie Lambert steered a shot harmlessly wide from Adam Lallana's seventh-minute free-kick, but despite their early dominance, they struggled to create further openings in a tepid first 25 minutes or so.
However, as the half wore on, keepers Simon Mignolet and Artur Boruc had to pay greater attention as the game started to open up. The Belgium international had to make a fine reaction save to keep out Jay Rodriguez's 32nd-minute snapshot and was then grateful to see Lambert scuff another effort wide of the far post four minutes later.
But he was even more relieved with three minutes of the half remaining when Lambert managed to control Steve Davis' driven cross, but failed to get any power into his shot. In the meantime, Boruc had got down to claim Adam Johnson's weak shot after John O'Shea had headed down a Sebastian Larsson corner.
Half-time substitute Connor Wickham's aggression immediately gave the home side greater presence, although it was the Saints who continued to make the better chances with central defender Jose Fonte powering in a 51st-minute header from a Davis corner which forced Mignolet into another good save.
However, Sunderland might have taken the lead within seconds when full-back Danny Rose, playing the final game of his loan spell from Tottenham - the Black Cats' opponents next weekend - fired the ball across the face of goal only for Danny Graham to completely miss his kick as the chance to claim a first goal in a red and white shirt passed him by.
It was the Black Cats who broke the deadlock in superb style with 22 minutes remaining. For once, the Saints found themselves pinned back inside their own penalty area and when Johnson slid the ball to the overlapping Bardsley, he smashed a right-foot shot across Boruc and with the help of a slight deflection off Jos Hooiveld, inside the far post.
But the joy was short-lived after Pochettino made a double change which paid off within four minutes.Ward-Prowse crossed from the left for Puncheon to power a header towards goal, only to be denied by the brilliance of Mignolet, but the Saints man reacted first to poke the rebound into the roof of the net.
Source: PA
Source: PA