Jurgen Klopp wrung the changes for the midweek Merseyside derby against Everton and won 5-2 to showcase their strength in depth. However, Salah, Alisson and Roberto Firmino were recalled for this one.
And their quality was on show again when Oxlade-Chamberlain finished off after being played in by Jordan Henderson on 35 minutes. The former Arsenal man watched the pin-point high ball all the way and beat Nathan Ake top open the scoring.
And it was 2-0 just before half-time when Keita poked home from close range following a superb backheel assist from Salah when surrounded by three Bournemouth defenders.
But it was roles reversed nine minutes into the second half when Bournemouth's Jack Simpson gave the ball away to Keita, who put Salah through to make it 3-0.
There was one sour note for Liverpool as they lost Dejan Lovren to injury in the first half but Klopp said he is hopeful it was not serious, while he praised his players as they stopped the opposition scoring for the first time in nine Premier League matches.
"It was a professional performance, controlled, scoring wonderful goals. We didn't want to make it exciting again so we wanted to control Bournemouth," Klopp told Sky Sports. "The most used word in the dressing room at the moment is clean sheet -- finally!
"Dejan Lovren was hopefully cramp but apart from that it was a perfect game. All round nearly perfect day."
Liverpool were in complete control for the entire 90 minutes despite never going above third gear while Eddie Howe's side have hit an alarming run of form.
The reverse was Bournemouth's fifth consecutive defeat in the Premier League. Liverpool stayed top and provisionally extended their lead over second-place Leicester to 11 points.