Roberto Firmino and Daniel Sturridge struck as Liverpool beat Bournemouth 2-1 on Sunday.
Firmino gave Liverpool the lead in the 41st minute at the Vitality Stadium, and Sturridge doubled their advantage a few minutes later.
Josh King then pulled one back in second-half stoppage time for the Cherries, but it was too little too late for Eddie Howe's men.
Until that point it was a comfortable afternoon's work for Liverpool, who moved level on points with Southampton in the Premier League table.
Jurgen Klopp made 10 changes from the side that beat Borussia Dortmund on Thursday night, but his side still dominated most of the first half, albeit creating very few chances.
Eventually, though, they opened the scoring as Firmino, the only man to keep his place in the side, was on hand to poke the ball into an empty net after Bournemouth goalkeeper Artur Boruc had palmed Sturridge's superbly improvised backheel into the Brazilian's path.
Then, on the stroke of half-time, Sturridge doubled their lead, and it was about as easy as it could get for the away side. Jordon Ibe floated a free-kick into the Bournemouth area in the second minute of stoppage time and Sturridge rose highest to head it into the bottom corner.
For all captain Tommy Elphick's talk of winning as many games as possible between now and the end of the season, Bournemouth looked for the most part like a side that had reached the 40-point milestone and were already planning their summer holidays.
Howe had made just one change from his side that beat Aston Villa last week to reach 41 points, but there was very little to speak of in an attacking sense from the home side in the first half.
In an attempt to get his side going the Bournemouth boss threw on striker Lewis Grabban for Junior Stanislas at the break, but it made little difference as Liverpool continued to dominate the early stages of the second half.
Boruc wasn't having his best afternoon in goal for the Cherries, and gave Firmino a great opportunity to make it 3-0 within two minutes of the restart, first spilling the ball out for a corner, before spilling the actual corner into the path of the Brazilian, who crashed the ball wide when he should have hit the target.
And after 53 minutes Sturridge had a glorious chance to add his second, but could only clip the outside of the post with a dink over Boruc after being played in by Joe Allen.
One of Klopp's changes was to hand a debut to goalkeeper Danny Ward in place of Simon Mignolet, and the Welshman was called into action on several occasions in the second half, denying King twice before making a great late save from Grabban's close-range header.
Sturridge had two great chances to add his second in the final few minutes, first hitting the woodwork then curling an effort just over the bar, before Ward was finally beaten in the 93rd minute as King took a touch just inside the area from Andrew Surman's ball before firing home.
Bournemouth then could have nicked a point at the death as Steve Cook headed just over, but Liverpool held on for the three points.
Player ratings
Bournemouth: Boruc (3), Francis (4), Elphick (4), Cook (4), Daniels (4), Ritchie (5), Gosling (5), Surman (6), Stanislas (4), Gradel (4), King (6)
Subs: Pugh (5), Grabban (6), Wilson (5)
Liverpool: Ward (6), Randall (6), Toure (6), Lucas (5), Smith (6), Allen (7), Stewart (6), Ibe (7), Ojo (7), Firmino (6), Sturridge (7)
Subs: Sakho (6), Lallana (5), Origi (5)
Man of the match: Joe Allen