The Reds boss made seven changes to the side that beat Everton in midweek as his side started the game in full control.
They took the lead just after the half-hour mark as Oxlade-Chamberlain got on the end of Jordan Henderson's long ball to poke the ball home for his first Premier League goal in two years.
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Keita then got in on the act as he linked up with Mohamed Salah, who provided an excellent assist for the Guinean to finish with the outside of his right foot to make it 2-0 at the break.
He linked up with Salah again at the start of the second half, this time turning provider, as the Egyptian slotted home with a deft finish across goalkeeper Aaron Ramsdale.
The result sees Liverpool consolidate their position at the top of the Premier League table as they extend their lead to 11 points before Leicester and Manchester City's later fixtures this weekend.
Slide through our gallery below for all the best photos from the Vitality Stadium.