Mikel Arteta's side escaped with a point despite trailing 3-1 with just two minutes of normal time left at the Emirates Stadium.
Martin Odegaard's goal sparked Arsenal's revival and Bukayo Saka snatched the equaliser in stoppage-time.
But, despite the thrilling escape, Arteta finished with his head in hands because the Gunners will travel to second placed Manchester City on Wednesday knowing it is Pep Guardiola's team who control the destiny of the title.
Arsenal are five points clear of City, but the champions have two games in hand due to their involvement in the FA Cup semi-finals against Sheffield United on Saturday.
If City win or draw against Arsenal and then win their remaining matches, they will be crowned champions no matter what the north Londoners do.
After blowing successive two-goal leads in damaging 2-2 draws against West Ham and Liverpool in their previous two matches, Arsenal at least showed tremendous spirit to reverse the trend.
"Obviously unhappy with the result. We made it very difficult again for ourselves," Arteta said.
"If you concede three like we did in a sloppy way it is very difficult to win, but the way we reacted I love my players more than ever.
"This young team reacts in a way that is incredible, when it is against the odds."
Arsenal keeper Aaron Ramsdale had handed Southampton's Carlos Alcaraz the opening goal after just 27 seconds.
In a painful twist, it was former Gunners forward Theo Walcott who doubled bottom-of-the-table Southampton's lead.
Gabriel Martinelli pulled one back for Arsenal before Duje Caleta-Car's headed Southampton's third.
Odegaard and Saka ensured Arsenal avoided a first defeat in 10 league games.
But City's six successive league wins put Arsenal under intense pressure and Arteta's young team are in danger of crumbling unless they can win their do-or-die showdown at the Etihad Stadium.
"It is not a final because there are still six games to go," Arteta said.
"We are down but they are more willing than anybody to win it. You can see that spirit in the dressing room but it is clear we have to do better defensively."
Arsenal's title hopefuls had the support of the last Gunners group to lift the trophy in 2004 as Patrick Vieira, Thierry Henry and Sol Campbell joined the crowd at the Emirates.
But even the presence of that iconic trio couldn't inspire them as the nerves tormenting Arteta's team were laid bare by Ramsdale's astonishing blunder inside the first minute.
Anxious Arsenal
Taking possession inside his own area, Ramsdale played a suicidal pass towards Thomas Partey that completely missed the midfielder on the edge of the area.
Alcaraz gleefully accepted the gift as he smashed his shot past the exposed Ramsdale.
The anxiety pulsing through Arsenal, both on the pitch and in the stands, was palpable and Southampton struck again after another calamitous error from the hosts in the 14th minute.
Partey gave the ball away to Alcaraz and his sublime pass caught Gabriel Magalhaes out of position, allowing Walcott to surge into the area and slot past Ramsdale with unerring precision.
Arsenal reduced the deficit in the 20th minute when Saka powered down the right flank and pulled his cross back towards Martinelli, who caressed a fine volley past Gavin Bazunu from 10 yards.
But Caleta-Car looked to have delivered the hammer blow in the 66th minute when he headed home from James Ward-Prowse's corner.
To their immense credit, Arsenal refused to surrender and Odegaard beat Bazunu with a superb curler from the edge of the area in the 88th minute.
Pouring forward in waves, Arsenal scented a remarkable escape and Saka poached the equaliser in the 90th minute with a clinical finish after Reiss Nelson's shot was pushed out by Bazunu.
Arsenal could have stolen the victory when Leandro Trossard fired against the bar to leave their title hopes hanging by a slender thread.
