It was Oxlade-Chamberlain's first appearance in the Champions League since suffering a serious knee injury against Roma in April last year.
He got off to the perfect start inside two minutes as he sent a low shot across the goalkeeper to give Liverpool a 1-0 lead.
He got his second just before the hour mark as he curled the ball with the outside of his foot to make it 2-0 to the Reds before they went on to win 4-1 thanks to goals from Sadio Mane and Mohamed Salah.
Speaking to BT Sports after the match, Oxlade-Chamberlain said: "I’ve definitely missed it. It’s nice to be back out there. It’s a special tournament to play in, a competition we all grew up wanting to play in one day.
"It was nice to be back out there [after] seeing the boys do so well in it last year. I was fortunate enough to get back involved on the bench for the big day in the final and watch the boys bring it home.
"It’s inspirational, it’s something I’ve wanted to get back to do. It’s just nice to be back in the starting line-up and try to put in a performance to help the team. To get a few goals was a bonus."
It will be interesting to see whether manager Jurgen Klopp opts to start Oxlade-Chamberlain against Tottenham at Anfield on Sunday.
The boss usually tends to favour a midfield trio of Fabinho, Jordan Henderson and Gini Wijnaldum, however, the performances of Oxlade-Chamberlain, Adam Lallana and Naby Keita this week is sure to give him a selection headache.
Looking ahead to the game this weekend, Oxlade-Chamberlain added: "We had a lot to improve on from the game at the weekend, same again tonight.
"But at the minute we’re getting results which are good and we can still improve. We’ll take a lot from this game.
"I’m sure the manager has got a lot of points he’ll be getting at us about to improve for the weekend, because we’re going need to get them right to put on a good performance and get the right result at the weekend."
Liverpool sit in second place in Group E after tonight's results, with first-placed beating RB Salzburg 3-2 away from home.