With defeat looming, Arsenal captain Martin Odegaard then curled home in the 87th minute and two minutes later Bukayo Saka scored from close range to spark bedlam in the stadium.
Arsenal laid siege to the Southampton goal but could not find the crucial winner.
Both sets of players collapsed to the turf at the final whistle after a result that helped neither side.
Arsenal lead the table by five points from Manchester City but they have now played two games more and have to go to the Etihad on Wednesday for what could be a pivotal clash.
Southampton remain bottom with 24 points.