Saints dominated the first half and carved out a 2-0 lead thanks to Jay Rodriguez's powerful early strike and a fine finish from Dejan Lovren in the 31st minute, but Fabio Borini quickly responded with a goal out of nowhere to give Sunderland hope.
The Black Cats improved after the break and drew level on 71 minutes when the in-form Adam Johnson slammed a powerful shot past Artur Boruc at his near post.
Both sides pushed for a winner in a frantic finale, when Gaston Ramirez and Lovren both had to be stretchered off, but they had to settle for a point apiece as Sunderland inched closer to safety and Southampton ended a difficult week with a frustrating draw.
Mauricio Pochettino's long-term future at Southampton may have been plunged into doubt following the resignation of Nicola Cortese as executive chairman, but the qualities he has developed at the club were fully in evidence as Saints started positively.
With Jack Cork anchoring the midfield, Steven Davis, Morgan Schneiderlin and Adam Lallana had the freedom to exploit the space between the red and white lines, and the visitors threatened to run riot.
They took the lead when Rodriguez made the most of Marcos Alonso's failure to clear his lines, teeing himself up to fire firmly into the bottom corner from the edge of the box with goalkeeper Vito Mannone helpless.
It could have been 2-0 with 18 minutes gone when Johnson deflected Luke Shaw's cross on to the post with Mannone wrong-footed, and Lambert wasted a glorious opportunity three minutes later when he shot across the face of goal from Schneiderlin's pass.
Rodriguez should have doubled his tally with 29 minutes played when Rickie Lambert robbed Wes Brown after the defender took a poor first touch and fed him, but he shot tamely at Mannone.
But the keeper was beaten again two minutes later when central defender Lovren met Davis' corner ahead of Brown and volleyed home.
However, seconds later Johnson crossed from the right for Borini to control and scuff a shot past keeper Boruc, who got a hand to the ball, but could not keep it out.
The Saints continued with their progressive approach in the second half and Davis fired over from distance full-back Shaw was allowed to run from his own half and thump a shot into Mannone's midriff.
Fellow defender Calum Chambers called up Mannone once again with a speculative 55th-minute effort, and the Italian needed two attempts to collect Rodriguez's effort seconds later after Schneiderlin and Lallana had capitalised on Brown's wayward pass.
The keeper denied Lovren and Shaw again within seconds as the hour-mark arrived, and he was relieved to see Rodriguez fire into the side-netting under pressure from Phil Bardsley after Lallana and Lambert had combined.
Borini thought he had levelled after being played in by substitute Craig Gardner with 64 minutes gone, but he did so from an offside position and the strike was correctly chalked off.
But they were not to be denied and Gardner was the provider once again with 19 minutes remaining when he fed Johnson on the right and saw him smash a rising shot past Boruc's less than effective defences and into the roof of the net.
The Poland international saved from Gardner and fellow substitute Steven Fletcher in quick succession as Sunderland went for broke, and it was the Saints who were more grateful to hear the final whistle after having substitute Ramirez and Lovren carried off within seconds of each other.