A late Josh King strike saw Liverpool and Bournemouth play out a hard-fought stalemate under the lights at Anfield.
The Cherries took the lead earlier in the tie courtesy of a howler from Liverpool midfielder Georginio Wijanldum, who played a stray back-pass into the path of Benik Afobe who slotted the ball home with aplomb.
Liverpool responded through talisman Philippe Coutinho, who was threaded through by Roberto Firmino to slot home and become the joint top scoring Brazilian in Premier League history in the process.
The Reds then took the driving seat with Wijnaldum making up for his earlier error by turning provider and putting in a deft cross for Divock Origi to bury a header.