New signings Gabriel Jesus and Oleksandr Zinchenko made their debuts for Mikel Arteta's side on Saturday (AEST) and both made an impact, with Jesus catching the eye and Zinchenko providing the assist for the opening goal of the game.
Gabriel Martinelli was the beneficiary, heading in from close range, with Arsenal belatedly adding a second in the closing stages when Bukayo Saka's cross was deflected by Marc Guehi into his own net.
Palace had chances to equalise in the intervening period, forcing strong saves from Aaron Ramsdale, but he and Arsenal stood firm to earn their first three points of the new campaign.
Jesus immediately showed what he will bring to Arsenal by dancing through the Palace defence before seeing his shot deflected into the path of Martinelli, who wastefully missed the target.
Martinelli soon had his goal, however, as Saka's deep corner was headed back across goal by an unmarked Zinchenko for the forward to nod in.
Early opportunities were few and far between for Palace, but a golden chance fell to Odsonne Edouard before half-time and his header drew a strong save from Ramsdale down to his right.
Ramsdale was again called into action early in the second half, with Wilfried Zaha feeding Eberechi Eze, who aimed his finish too close to the England goalkeeper.
Arsenal invited pressure in the closing stages, but Palace could not capitalise and saw its hopes of rescuing a result dashed unwittingly by Guehi.