Eldin Jakupovic saved a stoppage-time penalty to ensure Hull picked up a priceless point in their relegation battle after a 0-0 draw with Southampton at St Mary's.
With the game heading for a stalemate, Southampton were given the chance to earn a somewhat undeserved victory in stoppage time, but Dusan Tadic saw his penalty saved by Jakupovic.
There was little other goalmouth action of note in the match, with Kamil Grosicki coming closest for the visitors early on as his free-kick hit the post.
The result sees Hull pull three points clear of the bottom three, with Swansea in 18th playing on Sunday at Manchester United, and condemns Sunderland to Championship football next season. Saints stay ninth.
An unchanged Hull were slightly the better side in a poor first half, and almost took the lead as early as the sixth minute. Grosicki curled a delightful free-kick over the wall towards the top corner, but the ball clipped the outside of the post and flew wide.
The hosts really struggled to find any rhythm, and did not muster a single shot on or off target in the opening period.
After the break, the action remained a little cagey. Harry Maguire was having a fine game for Hull, however, and made a crucial late block to deny Sofiane Boufal early in the second half.
Tadic then went close with a volley, before all the entertainment came in the final 10 minutes.
Firstly, Jakupovic made amends for a poor punch by racing out to block from Redmond, before Oumar Niasse blazed over from a good position down the other end.
Then, just seconds into stoppage time, Alfred N'Diaye clumsily bundled Maya Yoshida to the floor, leaving referee Mike Dean no option other than to point to the spot.
Tadic stepped up confidently, struck the penalty low to Jakupovic's left, but the Hull stopper superbly clawed the ball out and away from danger.
Substitute Michael Dawson missed a late header that would have completed a most dramatic final flurry, but Saints held on for the draw.
Player ratings
Southampton: Forster (6), Cedric (4), Stephens (6), Yoshida (5), Bertrand (5), Davis (6), Romeu (5), Boufal (5), Tadic (4), Redmond (5), Gabbiadini (6).
Subs: Long (5), Rodriguez (N/A), Sims (5).
Hull: Jakupovic (8), Elmohamady (6), Ranocchia (6), Maguire (8), Robertson (7), N'Diaye (5), Clucas (6), Markovic (6), Evandro (7), Grosicki (6), Niasse (6).
Subs: Huddlestone (6), Dawson (N/A), Henriksen (6).
Man of the match: Harry Maguire