Belgian forward Benteke, playing his second Liverpool game following his big-money close-season transfer from Aston Villa, scored the game's only goal in the 26th minute despite Philippe Coutinho's involvement from an offside position.
Bournemouth had earlier had a goal ruled out, rather unluckily, and the south coast side impressed with their willingness to attack at every opportunity.
Liverpool joined Manchester City, Manchester United and Leicester City on six points from two games but James Milner said the new boys had given them a stern test.
“We knew it'd be tough against a team that have just come up,” Milner told Sky Sports.
“They lost their first game but they had a positive performance and we knew it'd be tough. They're a good team, they play football, they like to press high.
“We know we can play better but it's two wins out of two and there's still room for improvement.”
Bournemouth scored 98 goals in winning promotion last season and their refreshing, attacking intent contributed to an exciting opening to the game.
Having failed to score in their first-ever top flight game against Villa last week, Bournemouth were unlucky to have Tommy Elphick's header ruled out for a foul on Dejan Lovren.
Liverpool then began to assert their authority but their goal should not have been allowed.
Jordan Henderson's teasing cross evaded everyone - including the desperate lunge of Coutinho who was clearly lingering in an offside position - before Benteke converted his 12th goal in 13 league matches at the far post.
Henderson nearly added a spectacular second minutes later but his dipping shot clipped the crossbar before Coutinho flashed a good chance past the post.
As in the first half, Bournemouth started the second period strongly with Matt Ritchie going close on three occasions with a series of rasping long-range shots.
Liverpool handed an Anfield debut to attacking midfielder Roberto Firmino but the Brazilian made little impact following his introduction in the 70th minute.
Bournemouth continued to press for an equaliser but Benteke should have doubled Liverpool's advantage, scuffing a close-range shot against the crossbar in added time.
Liverpool, one of four teams to win their opening two fixtures, travel to Arsenal next while Bournemouth, who have yet to score in their opening two matches, visit West Ham United.
Original source: Benteke goal lifts Liverpool