The Reds dominated, creating chance after chance as they left Palace in tatters before the break. Striker Michael Owen was guilty of wasting the most clear-cut chances and could have had a hat-trick by the interval.
In the tenth minute Owen latched onto a lovely Bruno Cheyrou lay-off only to chip his shot over the keeper but past the far post.
Then, after neat inter-play between Emile Heskey and El Hadji Diouf, the ball fell to Owen five yards out in the 22nd minute but the controversy-dogged striker could only fire his shot high and wide of the mark.
An unpredictable Diouf looked the most dangerous Liverpool player as he enjoyed a free role behind the two strikers and he forced a tired Danny Granville to be substituted after just 36 minutes.
Palace brought on another striker in Dougie Freedman to combat the Liverpool onslaught and after the break it was the former Nottingham Forest striker who showed his class to set up a rare Palace attack.
In the 55th minute Danny Butterfield whipped in a cross from the right that was flicked on by Dele Adebola for Julian Gray to silence the home fans with a well-struck volley past a stranded Jerzy Dudek.
A mazy run by Gray bamboozled the Liverpool defence and as he crossed for the unmarked Adebola, Stephane Henchoz bundled the ball into his own net at the near post.
Ten-men Palace hung on for victory with keeper Cedric Berthelin crowning an impressive performance with a clean sheet.