Arsenal scored three goals in the opening 13 minutes, the fastest a team have taken a 3-0 lead in a Premier League match since the Gunners did so themselves seven years ago.
Nacho Monreal netted the first from Granit Xhaka's corner before the defender produced two assists for Alex Iwobi and Laurent Koscielny.
Alexandre Lacazette made it 4-0 on 22 minutes, latching on to Mesut Ozil's delightful flick for Arsenal's 500th PL goal scored by a Frenchman.
Monreal went off injured before half-time and, after the break, Petr Cech was denied a 200th PL clean sheet when Luka Milivojevic netted a consolation goal.
After inflicting Palace's first away defeat in six matches, Arsenal sit two points behind fifth-placed Tottenham Hotspur. The Eagles drop to 13th.
Arsenal: 30 Jan v Swansea (A)
Crystal Palace: 30 Jan v West Ham (A)