Although Palace went into the match without a defeat in their previous eight top-flight outings, Arsenal were well in charge for the majority of the first half and were fully deserving of the opening goal through Shkodran Mustafi in the 25th minute.
They stay sixth, level on points with Spurs, while Palace stay 16th.
Arsenal's Alexis Sanchez celebrates scoring their third goal.
After Sanchez scored twice against Crystal Palace, the Arsenal manager was asked whether he was concerned he may lose the Chilean at the end of the season.
The ball was played back towards the right side of the area where Alexandre Lacazette drew a good save from Julian Speroni only for the ball to fall to Mustafi who finished neatly with a first time shot.
USA embassy announces end to visa crisis with Turkey
Meanwhile, the Turkish Embassy in Washington D.C. has also lifted visa restrictions for the USA citizens. Both countries restarted visa issuances in November, but only on a limited basis.
Six minutes later, Arsenal would have been two up but for Speroni who produced an excellent, one-handed reaction save after Ozil had latched onto Sanchez's superbly weighted through ball.
"We'll see when he [Wenger] speaks to me but I'm sure it will get done, yes", said the midfielder after the match.
After Townsend's well-worked equaliser assisted by a pinpoint Wilfried Zaha cross had changed the game's complexion, Arsenal's nerves were settled only when Palace striker Christian Benteke hit a poor clearance out of defence, a mistake that ended with Sanchez rifling home the visitors' second in the 62nd minute.
When he half-heartedly cleared a corner to Calum Chambers, the defender returned possession to the Palace box and watched as Lacazette and Sanchez combined to create space for the latter to strike into the bottom left corner. Great finish; can Arsenal really think about cashing in on him next month?
89' - GOAL! Crystal Palace 2-3 Arsenal (Tomkins) Over comes the corner and at the back post, Tomkins climbs above Koscielny to head down and in!