Well into the four minutes of added time and with Harry Redknapp's outfit trailing 2-1, defender Higginbotham was well placed at the far post to send home a dramatic equaliser.
This six-pointer lived up to expectations with Fitz Hall putting the Eagles in front midway through the first half only for Peter Crouch to reply immediately from the penalty spot after Tony Popovic had handled.
Then on 58 minutes a brawl between Uruguayan defender Gonzalo Sorondo and Crouch saw both red-carded.
With so much at stake both sides started nervously. Perhaps Southampton settled first and Crouch had an early chance with a hopeful scissor kick which thankfully for Palace went over the crossbar.
Henri Camara was looking pacey and on a couple of occasions made progress across the byline delivering low crosses into the goalmouth that Palace were able to clear.
Olivier Bernard also did well with a low cross but the Southampton were lacking attacking options to capitalise.
Meanwhile, Palace's fortunes were mostly resting on Andy Johnson but the visitors were keeping a good eye on him.
Antti Niemi saved from Tom Soares and the Finnish keeper was called upon again, this time again keeping out Wayne Routledge's shot from the edge of the box.
This spell of pressure from Palace paid off on 35 minutes when Michael Hughes' free-kick just inside Southampton's half was poorly cleared by Higginbotham and Hall, with his back to goal, turned quickly to crash a 15-yard shot past Niemi's outstretched left hand.
Southampton replied straightaway as under no pressure Popovic misjudged the bounce of the ball and referee Howard Webb spotted the Aussie defender putting hand to ball.
Crouch showed no nerves as he coolly struck the kick low into the left corner. After the break Palace were having the better of the proceedings as Hall shot wide, Aki Riihilahti got on to the end of Johnson's cross, but fired over before Iain Dowie sent on Nicola Ventola to add to his attack.
Within five minutes, the Italian, on loan from Inter Milan, repaid Dowie's faith in him when he slipped the offside trap and raced on to fire a low right-foot shot to restore Palace's league.
Routledge then had two stabs at goal which went wide and Ben Watson struck a ferocious 25-yard shot which whistled over the crossbar before Palace foolishly decided to bank on defence.
As the minutes ticked away it took an absolutely outstanding save from Gabor Kiraly in the final minute of normal time to prevent Camara from scoring.
Just as it seemed time was running out for Redknapp's lads, substitute Kevin Philips was given far too much space on the left side and the ex-Sunderland man struck a low cross over to the far post for Higginbotham five yards out to hit a life-saver.
It's all going to rest on the results next week and Palace will hope their London neighbours Fulham do them big favour by beating Norwich and of course Southampton fail to win against Manchester United.
But still above all this, Palace must get a result against Charlton.
Man of the Match: Fitz Hall - Outstanding in defence for Palace as he kept the dangerous Peter Crouch quiet and his coolness on the ball was the springboard behind the Eagles' attacks.