The victory took Arsenal back to the top of the table.
Oxlade-Chamberlain said: "It's something I want to add to my game - more goals - so it was nice to get two today.
"It's always an amazing feeling to score a goal and especially at a stadium like the Emirates and I'm glad I can help the team with two goals.
"It was a tough game against Palace and they made it hard for us in the first half.
"But in the second half we knew if we kept the tempo up and kept wearing them down then we'd get more opportunities and we did."
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