The Blues' first-half dominance counted for nothing as the Eagles entered the break in front courtesy of a superb long-range strike from Jefferson Lerma, but the visitors responded well and equalised less than two minutes into the second period when Conor Gallagher fired home from close range against his former club.
Chelsea huffed and puffed as the game drew to a close and they eventually blew the Palace house down thanks to two goals in stoppage time, with Cole Palmer setting up both Gallagher and Enzo Fernandez to help the Blues secure back-to-back away victories in the space of five days.
Victory for the Blues has somewhat eased the pressure on manager Mauricio Pochettino, who has seen his side climb up to 10th in the Premier League table, but the same cannot be said for Palace boss Roy Hodgson who has lost four of his last five games in all competitions and sees his team remain in 15th place, five points above the relegation zone.
More to follow.