James Vaughan struck the only goal for the Terriers in the 65th minute to lift them eight points clear of the relegation zone in Lillis's second game in charge following the sacking last week of Simon Grayson.
Town's win denied Palace the chance of climbing into the second automatic promotion place.
Holloway accused Alan Lee of using an elbow in the closing stages immediately after the final whistle and the Town striker was confronted by furious Palace players.
Ugly scenes unfolded as the players headed for the tunnel and stewards were required to diffuse several heated exchanges.
"I was on the pitch applauding our supporters because they played a huge role in what was a massive win," said Lillis.