After being frustrated by Tony Pulis' well-drilled Palace for the first 45 minutes, Arsenal found a way through when Santi Cazorla deftly picked out Oxlade-Chamberlain's run just after the break. The England winger controlled the pass delicately and lofted a neat finish over Palace goalkeeper Julian Speroni.
Oxlade-Chamberlain made sure of the three points with a run and emphatic finish on 73 minutes.
The 20-year-old was making his first Premier League start for the Gunners since their opening-day loss to Aston Villa. He did not waste the opportunity, and Oxlade-Chamberlain's two clinical finishes proved the difference between one point and three for the home side.
The victory stretched Arsenal's home unbeaten run in the league to 11 games and put Arsene Wenger's team two points ahead of Manchester City atop the table. City, who have a game in hand, will have their chance to respond when they entertain Chelsea on Monday night.
Arsenal were not at their most fluent best against Palace, but this was exactly the type of win a side with realistic title ambitions must be able to churn out. The doubts continue, but Arsenal continue to answer them.
Wenger started with a midfield five of Oxlade-Chamberlain, Cazorla, Mesut Ozil, Mikel Arteta and Lucas Podolski, employing Olivier Giroud to spearhead the Gunners' attack.
Arsenal's usual passing game ensued, but Palace's stubborn resistance and some notable contributions from Speroni kept them at bay.
The visitors were not without their chances. Arsenal goalkeeper Wojciech Szczesny made a fine close-range save to deny Cameron Jerome, and Palace occasionally looked threatening.
That said, once Oxlade-Chamberlain had put Arsenal ahead, the result never appeared in question. His second goal eased Arsenal nerves and allowed the home fans to enjoy the last 10 minutes without worry.
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As for Palace, this was never a fixture you would have expected them to win, but there was much to praise in their organisation and plenty of hope in their performance for the relegation battle to come.