Scorers: Bournemouth - Gosling (57); Liverpool - Sterling (20, 51), Markovic (27)
The England winger had endured a 22-game goal drought for club and country until he set Liverpool on their way to a 3-1 win with a close-range header.
Lazar Markovic grabbed the second before a trademark Sterling run ended with his fifth of the season to put the smiles back on the faces of supporters after their Old Trafford defeat.
Dan Gosling pulled a goal back and then rattled a post as the Championship leaders relinquished their 12-game unbeaten run.
The majority of the sold-out crowd arrived with expectations that their table-toppers could pile more misery on Brendan Rodgers and they almost took an early lead.
Left-back Adam Smith saw an effort blocked by Martin Skrtel before Callum Wilson side-footed wide having done all the hard work to create an opening.
After those escapes, Liverpool began to kick into gear, with Adam Lallana forcing Artur Boruc into a fine save from 20 yards. The visitors began to pin Bournemouth in their own half and that sustained pressure eventually told in the 20th minute when Jordan Henderson headed Markovic’s delivery across goal for Sterling to nod in.
It was no surprise when Liverpool doubled their lead seven minutes later. Philippe Coutinho’s low shot was kept out by Boruc but the ball fell straight to Markovic, who calmly chalked up his first Liverpool goal.
Sterling doubled his tally in the 51st minute when he picked up a pass from Lallana and twisted and turned past Cherries captain Tommy Elphick before finding the bottom corner.
Reds goalkeeper Brad Jones had enjoyed a quiet evening until the 57th minute, when he failed to cover himself in glory as the hosts pulled a goal back, Gosling stepping through two challenges before squeezing a shot past the Australian.
Former Aberdeen winger Ryan Fraser watched a looping header fall wide, Gosling crashed an effort off Jones’ other post and Ritchie drilled a shot across goal as the Cherries bowed out with their heads held high.