Oxlade-Chamberlain was delighted as he scored a brace on his return to the starting line-up as the Gunners reclaimed top spot in the Premier League at Emirates Stadium on Sunday afternoon.
Arsene Wenger's side recorded their eighth win from their last nine matches and extended their unbeaten run to 10 games in all competitions to go back to the summit by two points ahead of Monday night's clash between second-placed Manchester City and Chelsea, who are in third.
But the defeat left Palace just one point above the relegation zone alongside West Brom on 23 points.
Man-of-the-match Oxlade-Chamberlain, who played alongside Mikel Arteta in central midfield, told Sky Sports 1: "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."
After a goalless first half, Oxlade-Chamberlain was found at the far post by Santi Cazorla's sublime pass over the top, controlled it well and chipped it over diving Palace keeper Julian Speroni from close range on 47 minutes.
Oxlade-Chamberlain doubled the Gunners' lead after 73 minutes after playing a clever one-two with Olivier Giroud then powering into the Palace box before beating Speroni with a powerful low shot.
Despite a tough opening half, Oxlade-Chamberlain was pleased his side dug in hard after the break.
He added: "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."
The 20-year-old midfielder returned from a serious knee injury - which had sidelined him since August - last month and fired home his first two goals of the season for the Gunners.
He said: "It was really nice to get a start. Obviously it was my first start since my injury on the first day of the season it was nice to get out there and in the midfield - it's nice that the boss has faith in me there."
Arsene Wenger praised match winner Oxlade-Chamberlain and said he could be important player for the club if he continues to impress as he did on Sunday.
He said: "We knew Crystal Palace are physically strong and we had to be intelligent, patient and take our chances.
"Oxlade-Chamberlain got us two great goals for us today and I'm very happy for him as he was out for four months this season and he had shown today that he can be a very important player for us."
The Gunners boss added: "Sometimes you have to be patient to create space and I think he used it very well when the opportunity was there and he has that kind of surge to come from deep midfield to be dangerous.
"For a young player like that he has shown that he will (keep his favoured midfield position)."
Wenger's side enter an important month in their search for silverware and, next up they face a daunting schedule including Premier League and FA Cup tussles with Liverpool, a league visit from Manchester United and the opening leg of their Champions League tie against holders Bayern Munich.
Oxlade-Chamberlain is confident they can keep their run going and said: "We've got a lot of hard fixtures but (have to take it) one step at a time.
"We've got a really big game at Liverpool away and we're looking to put this one behind us and take the positives from it and prepare to hopefully go and get three points from Liverpool."