Alex Oxlade-Chamberlain had given Jurgen Klopp's side the lead with his league goal since January 2018 before Keita added a second just before half-time.
Mohamed Salah made it three shortly after the break, and the Reds kept a rare clean sheet, ending a run of 13 matches in all competitions without one.
Liverpool moved 11 points ahead of second-placed Leicester City, who play on Sunday, and 14 clear of champions Manchester City ahead of their derby clash with Manchester United later in the day.
After a low-key start, Bournemouth lost defender Nathan Ake to an apparent hamstring injury following a challenge on Salah just after the half-hour mark.
And Liverpool took full advantage moments later when captain Jordan Henderson lifted a high ball over the top of the reshuffled Bournemouth defence and Oxlade-Chamberlain cushioned a first-time finish past goalkeeper Aaron Ramsdale
Liverpool suffered an injury setback of their own when Dejan Lovren departed clutching the back of his leg, but the Reds added a second goal on the stroke of half-time.
A superbly crafted team move culminated in Salah's backheel for Keita, who poked inside the right-hand post.
Liverpool then ended the game as a contest nine minutes into the second period when Jack Simpson lost possession to Keita, who returned the first-half favour and fed Salah to apply a cool finish.
Bournemouth's day got worse when leading marksman Callum Wilson limped limped off - also seemingly suffering with a hamstring problem - and Liverpool cruised through to full-time.