Nacho Monreal, on his return from a month long lay-off, gave his side an early advantage and with not even 15 minutes on the clock the full-back had also grabbed two assists, after setting up Alex Iwobi and Laurent Koscielny, before having to limp off with an ankle injury.
Cote d'ivoire's Wilfried Zaha and Mali's forward Bakary Sako were on parade for the Eagles throughout the duration of the game but could not save Roy Hodgson's side from the defeat.
The return of German playmaker Mesut Ozil, who laid on a handsome backheeled assist for Lacazette's goal, also helped Arsenal fans to forget the absence of Sanchez, who was left out of the squad for a second straight game.
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Palace were particularly guilty of poor defending at corners at the Emirates Stadium, which led to the goals from Monreal and Koscielny.
Crystal Palace had struggled to clear their lines and when they did get a foot into a challenge they quickly surrendered possession, it ultimately paved the way for Monreal to burst down the left-hand side of the penalty box and tee-up the Nigeria worldwide who bundled the ball into the back of the net from six-yards out. "I really enjoyed that little spell in the first half".
The win is Arsenal's first in 2018 and keeps them in sixth.
Arsenal will now switch their attentions back towards League Cup affairs and their home clash against Chelsea in the semi-finals on Wednesday night.