Maya Yoshida put Southampton ahead with just six minutes left
Saturday’s stunning win at Chelsea had boosted Allardyce’s hopes of steering his side to safety.
And when Christian Benteke put the Eagles ahead in the 31st minute, they looked on course for another win.
But manager Allardyce and his players were left fuming when referee Roger East allowed Nathan Redmond’s 45th-minute equaliser to stand, believing Wilfried Zaha to have been fouled in the build-up.
After surviving heavy home pressure, the visitors then wilted in the 84th minute when Yoshida bundled home from close range. Ward-Prowse piled on the agony a minute later with another first-time finish from inside the box.
Allardyce insisted he had been on alert at the training ground for any signs of complacency following the win over leaders Chelsea.
James Ward-Prowse scored seconds late to ensure three points for Southampton
He warned of the difficulty of following such a success, and the opening moments suggested the Palace players were in danger of letting standards slip, allowing Shane Long an early sight of goal.
The Saints striker combined well with Redmond on the left and worked his way into the box before sending a shot across the face of goal and only just beyond the far post.
That was an early warning shot and the manner in which the home side had eased their way through was a reminder that Allardyce had been forced to rejig his back four following the weekend injuries to James Tomkins and Scott Dann.
Redmond provided another scare when he headed against the post but Palace grew more secure as the half wore on before making the breakthrough.
Yohan Cabaye started the move with a strong tackle and Andros Townsend ended it with a low cross that was turned in by Benteke.
How the Premier League table would look if two points were awarded for a win
Wed, April 5, 2017
How would the Premier League table look if two points were awarded for a win rather than three? Correct up until 10pm on April 5 2017
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That was promising, but Saints were level when Redmond scored from Steven Davis’s cross, despite Palace complaining Zaha had been fouled.
That gave the home side the momentum they needed after the restart as two goals in as many minutes killed off the visitors.
SOUTHAMPTON (4-2-3-1): Forster 6; Soares 7, Stephens 6, Yoshida 6, McQueen 6; Davis 7 (Hojbjerg 87), Romeu 7; Tadic 6, Ward-Prowse 7, Redmond 8 (Rodriguez 90); Long 7. Booked: Romeu, Soares. Goals: Redmond 45, Yoshida 84, Ward-Prowse 85. NEXT UP: West Brom (a), Sat PL.
Crystal Palace (4-2-3-1): Hennessey 6; Ward 6, Kelly 5, Sakho 5, Schlupp 6 (Delaney 58, 6); Cabaye 6 (Sako 46), Milivojevic 6 (Flamini 88); Townsend 6, Puncheon 6, Zaha 6; Benteke 7. Booked: Benteke. Goal: Benteke 31. NEXT UP: Arsenal (h), Mon PL.