It was goalless at half time, but the midfielder struck twice in the second half to break Palace's resistance.
Oxlade-Chamberlain returned to the Arsenal team in the recent 4-0 win against Coventry City in the FA Cup, and he has now revealed that it was "nice" to get back on the pitch as the Gunners go in search of silverware.
"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," Oxlade-Chamberlain told BBC Sport.
"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."
Arsenal play Liverpool away from home next weekend.