The drama came late in a tense contest at St Mary's Stadium when Maya Yoshida - making his 100th Premier League appearance - was hauled down by Alfred N'Diaye in the area.
Jakupovic was the hero though, as he kept out Dusan Tadic's effort to move Hull three points clear of the relegation zone - condemning Sunderland, who lost at home to Bournemouth, to the drop in the process.
Prior to the penalty incident, it was Hull - without a win at Southampton since 1951 - who had the better of an underwhelming encounter, Kamil Grosicki hitting the post from an early free-kick was the closest either side had come to breaking the deadlock.
In a cruel twist of fate it appeared that Hull's losing streak on the road would be extended to six games when referee Mike Dean pointed to the spot, but Jakupovic ensured the Tigers returned to Yorkshire with a share of the spoils.
2 - Hull picked up only their second away point in the top-flight this season under Marco Silva (in eight away games). Battle.— OptaJoe (@OptaJoe) April 29, 2017
The Tigers remain with a solitary league win to their name on the road this term, but Silva's side showed plenty of endeavour from the off, and Fraser Forster was left flat-footed as Grosicki's dipping free-kick clipped the left-hand upright six minutes in.
Silva was able to call on Oumar Niasse after the Everton loanee successfully appealed his red card against Watford, and only a last-ditch challenge from Jack Stephens stopped the Senegal forward getting in on goal moments later.
With the hosts failing to offer a notable threat, Grosicki's tame effort on the stroke of half-time brought up the game's first attempt on target.
Hull captain Harry Maguire was a resolute presence at the back throughout and was on hand to halt Sofiane Boufal's excellent run shortly after the restart as the Saints stirred, while Forster produced an instinctive stop to prevent Grosicki latching onto Niasse's dangerous cross at the other end.
Southampton rallied late on - Maguire and then Jakupovic doing well to deny Tadic from close range after the goalkeeper had failed to deal with a corner.
But Jakupovic's best was saved for the very end as N'Diaye was pulled up for a clumsy challenge on Yoshida, only for the Swiss keeper to guess correctly and deny Tadic low to his left as Silva's remarkable escape act draws closer.