The England international broke the deadlock in the 47th minute at the Emirates Stadium with a lofted effort after collecting Santi Cazorla's clipped pass.
And Oxlade-Chamberlain, who was making his first Premier League start since August 17, made sure of the points with a low strike under Palace goalkeeper Julian Speroni on 73 minutes.
Wenger deployed the 20-year-old in a central midfield role, and believes Oxlade-Chamberlain can have a future in that position - despite largely being recognised as a winger.
"I always believed that he could play wide and central, he has proven me right today by scoring the goals," the Frenchman said.
"But also the overall quality of his performance. It took him a while to get back because he was injured against Villa."
The win saw Arsenal move back to the top of the Premier League, and Oxlade-Chamberlain was thrilled to contribute.
He told Sky Sports: "It was nice to get the win today, it is always an amazing feeling to score a goal. I've been off the pitch for a while so it was nice to come back and help the team.
"It was a tough game but we knew that in the second half if we kept the tempo up we would get more opportunities and thankfully we did."
