But Allardyce's men struck back to earn a crucial point through Yohan Cabaye and Christian Benteke to claim what could yet prove a vital point.
They had looked at severe risk of relegation but manager Sam Allardyce - who recruited Shakespeare to his coaching team while England manager - has inspired such an improvement that survival looks a near certainty.
The Foxes have themselves risen dramatically up the table with Craig Shakespeare guiding them to six straight wins in all competitions.
Craig Shakespeare is hopeful talismanic defender Wes Morgan will be fit to return for Leicester City's Champions League quarterfinal second leg against Atletico Madrid on Tuesday.
Crystal Palace produced a stunning comeback to draw 2-2 against Leicester City on Saturday.
Crystal Palace (4-2-3-1): Hennessey; Ward, Kelly, Sakho, Schlupp (Van Aanholt 67); Cabaye, Milivojevic; Townsend, Puncheon, Zaha (McArthur 84); Benteke. Permission to use quotations from this article is granted subject to appropriate credit being given to www.theeagleonline.com.ng as the source.
Commenting on the centre-back's contract with Palace, Allardyce told the Liverpool Echo: "There isn't a clause because his deal was done in the Bournemouth corridor by me after we had won 2-0, and Steve (Parish) finishing the negotiation over the phone to try and secure Mama".
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All six of Huth's Premier League goals for Leicester have come away from home. But they had to wait until the final moments of the first half before another clear opening came their way when Andros Townsend was released into the area by Ward.
Five wins out of six going into yesterday's game was impressive form.
Wilfried Zaha has assisted nine goals for Crystal Palace in the Premier League this season, equalling the record by an Eagles' player in a single PL campaign (Wayne Routledge, nine in 2004-05). Leonardo Ulloa's effort appeared to hit a Palace hand before the striker flashed a volley just wide.
"In terms of recovery we've had this fixture planned for a while".
- The Foxes scored from their first shot in the game, while Robert Huth's goal proved to be Leicester's only shot in the first half.
Premier League rules dictate that eight of those in a first-team squad must be considered home-grown, which in the present climate can include those from within the European Union who are ineligible to play for England, Scotland, Wales, Northern Ireland or Ireland.
"We're faced with the prospect of having a team with eight home-grown players, none of whom qualify to play for the Home Nations", said Parish.