Early strikes from Carlos Alcaraz and Theo Walcott were not in the script for the table-toppers, who cut the deficit in half through Gabriel Martinelli before the Saints restored their two-goal advantage through Duje Caleta-Car.
However, a frenzied final 10 minutes saw Martin Odegaard and Bukayo Saka give Arsenal hope of pulling off another one of their sensational comebacks, but both sides ended up ruing what could have been at the full-time whistle, which signalled the end of one of the craziest Premier League games of the season.
Emulating South Coast counterparts Bournemouth at the Emirates, Southampton stunned the home crowd into silence after just 27 seconds, as Aaron Ramsdale did his best David de Gea impression to hand Alcaraz the opening goal on a plate.
The Arsenal number one attempted to play out from the back to Oleksandr Zinchenko, but Alcaraz anticipated his pass, stole in and picked out the far corner from the edge of the D with Ramsdale in no man's land.
Mikel Arteta's men only needed to beat the basement side to seal their top-four finish, but a disjointed XI were the architects of their own downfall, and their uphill task became even steeper with 14 minutes gone.
The effervescent Alcaraz went from goalscorer to provider during a Southampton break, playing a perfectly weighted through ball through to ex-Arsenal man Walcott, who sped away from Gabriel Magalhaes and slotted home into the corner.
A Zinchenko-engineered team huddle would appear to galvanise the shell-shocked Gunners, though, and the hosts reduced the deficit just six minutes later as their two danger men combined.
Saka did brilliantly to get to the byline and cut back for Martinelli, who clinically side-footed a volley into the centre of the goal, which had been exposed as Gavin Bazunu went to protect his near post.
A slight lull followed after a frenzied opening 20 minutes, although Odegaard should have done better with a free header in the 28th minute - nodding harmlessly over the bar before Southampton were forced into a change.
Jan Bednarek suffered a sickening fall over Martinelli onto the back of his neck - staying down for a few minutes - and despite vociferously protesting with the medical staff, he was ultimately taken off for Caleta-Car.
Seven minutes of added time allowed Arsenal to huff and puff in search of a timely equaliser, and they came agonisingly close to their second when Ben White flicked on Saka's corner at the near post, but Alcaraz - the hero at both ends of the field - produced a brilliant headed clearance off the line to preserve Southampton's lead at the break.
Arsenal's Granit Xhaka-less midfield were at sixes and sevens at the Emirates, but Arteta held off on making any half-time switches, while Ruben Selles took off star man Alcaraz for Lyanco in a switch to a five-man backline.
Selles was evidently anticipating a Gunners onslaught in the second 45, and the Saints unsurprisingly spent the next 20 minutes camped inside their own half, but futile Arsenal attacks were quelled with ease.
During a rare foray forward in the 67th minute, Southampton won a corner in front of the away end, and Armel Bella-Kotchap flicked on James Ward-Prowse's delivery to the back stick, where Caleta-Car arrived unchallenged to head home and restore the Saints' two-goal lead.
An unwanted piece of history was written for Arsenal, who became the first table-topping team to concede three goals to the side starting the day at the bottom of the table, but there was something to cheer for the fans that stayed in the 88th minute, as Odegaard played a one-two with White and managed to bend a curler into the far corner.
The captain's strike would seemingly be nothing more than a mere consolation, but another astonishing Arsenal comeback was almost complete in the 90th minute, as Bazunu could only parry a Reiss Nelson effort into the path of Saka, who converted to level the scores in incredible fashion.
Arteta's men were gifted eight minutes of added time to try to find an improbable winner, which so nearly came in the second thanks to a mazy run and shot from Leandro Trossard, whose thunderous strike hit the bar and sailed over.
Southampton survived a couple of goalmouth scrambles and a wild Thomas Partey strike to hold on for a point, but the atmosphere soon fell flat, as a draw did little for either side's end-of-season goals.
Arsenal now boast a five-point lead over Manchester City in first place, but the champions have two games in hand and will host Arteta's men at the Etihad on Wednesday in a season-defining top-of-the-table clash.
Meanwhile, Southampton remain cut adrift in 20th place with 24 points, three adrift of safety before they host fellow relegation candidates Bournemouth next Thursday.