With Glen Johnson out injured, and Simon Mignolet rested, Martin Kelly came in at right-back, whilst Brad Jones made a rare appearance in Liverpool’s goal.
Victor Moses replaced Raheem Sterling in Liverpool’s attack, but was switched to the left side, and broke the deadlock on 26 minutes after a sluggish start from the Reds
Moses turned on the edge of the area to hit home a well place, although perhaps slightly scuffed, shot which rolled in past Cherries goalkeeper Lee Camp.
The Nigerian had a much improved performance to that which he produced in the previous round at home to Oldham Athletic, making exciting runs and getting involved in the game.
Liverpool looked in third gear throughout the game, but their quality prevailed and Daniel Sturridge doubled the lead on the hour mark.
Luis Suarez’s through ball was latched onto by Sturridge, who’s one-touch finish was stuck away past Camp for a trademark Suarez/Sturridge combination goal.
Sturrdige later almost lobbed Camp from the edge of the area, hitting the top of the bar with his effort.
At the back, Liverpool looked shaky at times, whilst Jones had several uncomfortable moments, flapping at crosses.
Aly Cissokho again looked lost at left-back, giving away possession consistently, tracking back slowly and giving away needless free-kicks.
However, it was a win, and that’s all Liverpool came to the south coast for.
Bournemouth: Camp, Francis, Elphick, Ward, Daniels, Ritchie (Fraser 72), O’Kane, Arter (Pitman 77), Pugh (Rantie 72), Surman, Grabban.
Substitutes: Allsop, Cook, Pitman, Harte, MacDonald, Fraser, Rantie.
Liverpool: Jones, Kelly (Flanagan 72), Skrtel, Toure, Cissokho, Gerrard, Henderson, Moses (Sterling 83), Coutinho (Alberto 83), Suarez, Sturridge.
Substitutes: Mignolet, Alberto, Aspas, Sterling, Ibe, Flanagan, Sama.
Referee: Lee Probert
— thanks to @MostarLFC