The Belgian opened his account for the Merseyside outfit when he latched onto the end of a Jordan Henderson cross after 26 minutes, sealing Liverpool’s second Premier League win in as many matches.However, starting from an offside position, Philippe Coutinho had made an unsuccessful bid to connect with the ball before it reached Benteke, which appeared to influence the decision-making of Bournemouth goalkeeper Artur Boruc.
Under new rules introduced for the 2015-16 season, Coutinho should have been flagged for offside, but the goal was allowed to stand.
Bournemouth boss Eddie Howe, who saw a Tommy Elphick effort disallowed after five minutes, will be encouraged by how his team responded in the second half, though.
After Matt Ritchie had found a post with a powerful drive, Eunan O’Kane also went close, but the home side held on to join Leicester City and the two Manchester clubs as the Premier League’s only sides to have taken maximum points from their opening two fixtures.
Liverpool were unchanged from their opening-weekend victory at Stoke City, but it was Bournemouth – who brought Max Gradel and O’Kane in for Marc Pugh and Dan Gosling – who looked to have taken the lead after five minutes.
Elphick rose above Dejan Lovren to head home from a corner, but the Bournemouth captain was deemed to have impeded the Croatian defender in climbing for the ball, prompting referee Craig Pawson to award Liverpool a free-kick.
Bournemouth felt hard done by but did not look overawed by the occasion on their first Premier League away fixture, and Liverpool – despite dominating possession – were struggling to carve out any clear-cut opportunities.
That was until Benteke met Henderson’s left-wing delivery to score at the far post, although Coutinho could count himself lucky not to have thwarted the move with his own attempt to convert.
Benteke’s goal came after a spell of Liverpool pressure and the hosts continued to threaten, with Henderson fizzing a wonderful first-time effort agonisingly over moments later.
After a quiet start, Liverpool had found their stride, and Coutinho should have done better when he guided the ball well wide of the left-hand post from 12 yards two minutes from the interval.
James Milner failed to get a clean connection on a Jordon Ibe cross early in the second half, sending the ball trickling wide, and – after Liverpool captain Henderson had left the field to be replaced by Emre Can – Bournemouth started to look capable of finding an equaliser.
Ritchie rifled a fierce strike against the outside of the right-hand upright, before O’Kane found the side-netting from a tight angle.
However, Liverpool weathered that storm to hold out for the full three points, just failing to add further gloss on the victory as Benteke hit the crossbar from close range in stoppage time.