Goals from Michael Olise and Jean Philippe-Mateta saw Patrick Vieira's side dispatch the Lions in Bermondsey, securing their berth in the FA Cup's next stage.
It's not long until Palace find out who they'll face, either, with the fourth round draw taking place on Sunday, 9th January. Full details are below.
Fourth round draw details
Date: Sunday, 9th January
Time: After West Ham v Leeds United (approximately 16:50 GMT)
How to follow
The draw will be shown live in the United Kingdom on ITV. David James and current Arsenal Women's captain Leah Williamson will pick out the 32 balls.
It will also be broadcast live via the FA Cup social media channels.
Alternatively, supporters can stay tuned to cpfc.co.uk, the official Palace app and our social media channels to find out our opponent shortly after they're drawn.
What ball number are Palace?
When is the FA Cup fourth round?
Fixtures will take place between Friday 4th and Monday 7th February.
Fourth round rules
There will be no replays in the 2021/22 FA Cup fourth round.
Outcomes will be decided on the day of the match, so games will go to extra time and penalties if required.
VAR can only be used in ties held at Premier League club's stadia. It was therefore not be in place for Palace's third round clash away at Millwall.
When are the other rounds?
The following rounds will commence on the below dates:
Fifth round proper: Wednesday, March 2nd
Quarter-finals: Saturday, March 19th
Semi-finals: Saturday, April 16th
Final: Saturday, May 14th