AFC Bournemouth suffered a 1-0 defeat at Anfield, as they had an early Tommy Elphick goal controversially ruled out.
The Cherries had the ball in the net after just five minutes as Elphick headed home from an out-swinging corner, but referee Craig Pawson blew his whistle to disallow the captain’s early effort.
A second corner soon brought another chance, as Joshua King headed Max Gradel’s whipped corner just over the crossbar.
Eddie Howe’s men had started well and Charlie Daniels galloped forward to cross into the near post, but the onrushing Callum Wilson was unable get a clean strike on the ball.
Liverpool then started to turn up the pressure. Christian Bentenke was quick to pick up a loose ball inside the Cherries’ half and fired just wide of Artur Boruc’s far post.
It was then that the home side took the lead. A short corner on the 26th minute was eventually crossed deep into the penalty area, and summer signing Benteke was on hand to tap home from close range.
The Reds then had chances to double their lead before the interval. Captain Jordan Henderson rocketed an effort just over from range, before Coutinho then fired wide from inside the penalty area.
The Cherries started the second half brightly, and Matt Ritchie cut in from the right flank and unleashed a shot to test Simon Mignolet early on.
The ball then presented itself once again to Ritchie just five minutes later, and the Scotland international fired a strike tantalisingly wide of the Liverpool post.
The home side continued to pile on the pressure but resolute defending, including heroic blocks from Andrew Surman and Daniels, kept them at bay.
With just five minutes to go the Cherries had the chance to draw level. A dangerous corner found the head of Francis, but his effort looped high onto the roof of the net.
Liverpool then had an opportunity to double their lead just before the final whistle. But Benteke was denied as Boruc made a fantastic stop and tipped his close-range strike onto the crossbar.
Cherries: Boruc, Francis, Cook, Elphick (c), Surman, Gradel (Smith, 80), Daniels, Wilson, King (Tomlin, 60), Ritchie, O’Kane (Gosling, 86)
Not used: Pugh, Mings, Federici, Distin