The Belgian arrived from Chelsea on loan until the end of the season in January and the striker made an instant impact, diverting home from James McArthur's mishit shot five minutes before half-time.
Leicester continued to push forward after having the majority of the chances and Jonny Evans levelled the score with a close-range finish midway through the second half.
But a late brace from Wilfried Zaha and Luka Milivojevic netted from the penalty spot late to seal all three points as the Eagles climbed to 13th in the table and six points clear of the relegation zone.
It had been a tight and scrappy half of football as neither side created any chance of note in the opening quarter of an hour.
But Leicester soon sparked into life, with Harvey Barnes crossing from the left and Jamie Vardy glanced his header just wide of the post.
The Foxes were dominating possession and had most of the ball in Palace's half but soon found themselves behind.
James McArthur tried a speculative effort from 25 yards out and Batshuayi, hovering on the edge of the penalty box, reactly quickly to divert the shot past Kasper Schmeichel.
The Foxes came out of the blocks after the break and Christian Fuchs should have done better when he got on the end of Jonny Evans' cross but headed wide.
James Maddison and Harvey Barnes continued to show their talent on the left as Leicester searched for the goal to put them in front but they were stunned when McArthur supplied a cross to the back post and Zaha volleyed home.
Things soon got worse for the hosts when Jonny Evans brought down Jeff Schlupp and Milivojevic netted his seventh penalty of the season.
There was still time for a fourth in stoppage time when Jordan Ayew caught Evans in possession and sent Zaha racing in on goal. The Ivory Coast international struck his effort straight at Schmeichel but he could only palm it into his own net to pile more pressure on the under-fire French coach.
Team line-ups, match action and reaction
Leicester XI: Schmeichel, Ricardo Pereira, Evans, Maguire, Fuchs, Tielemans, Ndidi, Maddison, Ghezzal, Vardy, Barnes.
Substitutes: Soyuncu, Morgan, Gray, Iheanacho, Ward, Okazaki, Mendy.
Crystal Palace XI: Guaita, Ward, Tomkins, Sakho, Van Aanholt, McArthur, Milivojevic, Schlupp, Townsend, Batshuayi, Zaha.
Substitutes: Dann, Meyer, Kouyate, Hennessey, Ayew, Benteke, Riedewald.
Referee: Anthony Taylor (Cheshire)
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