The Eagles last tasted victory against the Blues in 2017, but they will undoubtedly be the happier of the two teams after coming from a goal behind to earn a valuable point on the road.
Chelsea took the lead just after the midway point of the first half following a quick counter-attack, with Cole Palmer once again being the provider as he teed up Nicolas Jackson to tap home from close range.
It was a first half that was largely dominated by the hosts, but Chelsea did not capitalise on their dominance as Oliver Glasner's side held firm after going a goal behind.
The Eagles then stepped up in the second half and equalised early on, courtesy of Eberechi Eze's superb whipped strike from the edge of the area.
Glasner's side grew in confidence and enjoyed a stronger second half in what became an evenly-contested second half between the two London clubs.
The away side almost grabbed all three points fifteen minutes from time as Daichi Kamada's strike was saved by Robert Sanchez, but in the end both sides had to settle for the draw.
CHELSEA VS. CRYSTAL PALACE HIGHLIGHTS
15th min: Chelsea 1-0 Crystal Palace (Nicolas Jackson)
Chelsea take the lead after a swift counter-attack!
The hosts break down the right through Noni Madueke, and his pass finds Palmer who delightfully prods the ball along the six-yard box for Jackson to tap home into an empty net.
53rd min: Chelsea 1-1 Crystal Palace (Eberechi Eze)
It's a bolt from the blue and the Eagles equalise in style!
After a blocked shot falls at the feet of Eze from just outside the penalty area, the midfielder takes the ball in his stride and he curls a delicious effort beyond the despairing dive of Sanchez.
MAN OF THE MATCH - COLE PALMER
The Chelsea talisman was once again instrumental for everything good going forward, and he grabbed his fourth assist of the season already with an inch-perfect pass for Jackson.
The Englishman created five chances in total, and once again his quality on the ball was head and shoulders above the rest of the field.
CHELSEA VS. CRYSTAL PALACE STATS
Possession: Chelsea 63%-37% Crystal Palace
Shots: Chelsea 13-9 Crystal Palace
Shots on target: Chelsea 7-3 Crystal Palace
Corners: Chelsea 4-5 Crystal Palace
Fouls: Chelsea 9-13 Crystal Palace
WHAT NEXT?
After the first international break of the season, Chelsea will travel to the south coast to play an unbeaten Bournemouth at the Vitality Stadium, while Crystal Palace will host Leicester City at Selhurst Park.