The midfielder opened the scoring after just two minutes and added a brilliant outside-of-the-boot finish in the second half, before Sadio Mane and Mohamed Salah wrapped up victory for the Reds in the Group E clash.
Here are five talking points from the game at KRC Genk Arena...
Ox announces Champions League return
Handed a start following his impressive performance off the bench against Manchester United on Sunday, it took Oxlade-Chamberlain just one minute and 50 seconds to make his mark against Genk.
Looking sharp and spritely from kick-off, the Liverpool midfielder collected a pass from Fabinho about 20 yards from goal, took a touch and fired a precision daisy-cutter into the far corner to notch the fourth-fastest goal in the club's Champions League history.
It was the Englishman's first strike since suffering a serious knee injury 18 months ago, but we didn't have to wait quite as long for his next one.
Indeed, the second arrived 55 minutes later and was even better than his first. Teed up on the edge of the box by the irrepressible Roberto Firmino, the Liverpool No.15 bent a looping effort over goalkeper Gaetan Coucke and in off the crossbar with the outside of his boot.
New midfield mix
Jürgen Klopp made five changes to the team that drew 1-1 at Old Trafford at the weekend and fielded a midfield trio of Fabinho, Oxlade-Chamberlain and Naby Keita which had never played together before.
Not that you would have known.
We have already highlighted Oxlade-Chamberlain's decisive contribution but the combative Keita also caught the eye on his first start since the 2-0 EFL Cup win over Milton Keynes Dons back in September.
His first pass of the match purposely came off his back (yes, his back) for Andy Robertson and the Guinean grew into the game from there.
The No.8 helped boss the midfield as he repeatedly won the ball and then showed his class in possession to help drive his team upfield.
With birthday boy Fabinho anchoring the midfield with typical aplomb - and stepping out to provide an assist - the trio have given Klopp yet more selection options.
Firmino still making jaws drop
We already know it, but it's worth stating once again: Firmino is class.
Just when you think you have seen it all from the Brazilian forward, he conjures something that still makes your jaw drop.
His outrageous rabona through ball for Mane on 25 minutes was one such moment. The heroics of Genk goalkeeper Coucke may have denied a picture-book goal but the skill itself was enough to make you drool.
Another moment arrived when he controlled a chest-height ball with nonchalant ease and flicked off a pass to keep Liverpool on the attack as if it was nothing. It was really something.
Oh, and the assist for Oxlade-Chamberlain's second goal and the inventive reverse pass in the build-up to Mane scoring Liverpool's third weren't bad either.
Salah's goalscoring return
An ankle knock ruled Salah out of Liverpool's 1-1 draw with United on Sunday but he was thrown straight back into action at KRC Genk Arena.
Double-marked by defenders Jere Uronen and Jhon Lucumi throughout the match, the Egyptian still managed to pop up with a clever assist for Mane and then topped that by scoring Liverpool's fourth goal in the closing minutes.
Having been picked out by Mane on the edge of the box, Salah showed strength to wriggle free of Lucumi before spinning between two defenders and prodding a shot beyond Coucke and into the back of the net.
Salah has now netted 19 goals for the Reds in the Champions League. Only Steven Gerrard has ever scored more for the club in the competition, with 30.
Like father, like son
And finally, a special mention must go to the stirring welcome Divock Origi received from the Genk fans when he came on as a substitute in the 80th minute.
Serenaded from the stands, it was a touching moment for a player who spent nine years at the Belgian side's academy before moving to Lille in 2010 at the age of 15.
His father, Mike, also represented the club from 1998 to 2002 and before the match Origi had spoken of how Genk holds a special place in his heart.
It appears the feeling is mutual.