Despite the dismissal of Michael Brown and the absence of a recognised goalkeeper for more than half the game, the visitors held on for a deserved triumph.
Palace, who went into the game on the back of three successive wins, had Tommy Black booked in the second minute after a foul on Zimbabwe international Ndlovu.
The 30-year-old winger was the first to threaten for the visitors when his shot from the left side of the penalty area flew wide before Allison's header was off target from Michael Brown's centre.
The Blades, unbeaten themselves so far this season, continued to impress in the early stages and Ndlovu's shot across the face of goal was kept out by the feet of Palace goalkeeper Matt Clarke after seven minutes.
Ndlovu got a reward for his endeavours when he curled a right-foot shot into the bottom corner after Shaun Derry was dispossessed by Michael Tonge in midfield.
Palace could have levelled after 24 minutes but Neil Shipperley fired a penalty straight at Paddy Kenny after Dougie Freedman was hauled down in the area following an impressive run from deep.
Freedman was forced off as a result of the challenge with Andy Johnson his replacement while Kenny was also struggling after a challenge with Derry.
He was eventually stretchered off just before the break to leave Neil Warnock with problems, as defender Phil Jagielka had to take the gloves as there was no goalkeeper on the bench.
But his side responded with another goal in stoppage time, Allison heading home Tonge's corner from close range.