Mohamed Salah brought his remarkable goal tally to 40 in all competitions this season season by netting once more in a 3-0 win over Bournemouth.
Only three times before has a Liverpool player reached the 40-goal mark, after Roger Hunt in 1961-62 and Ian Rush, who did it in both 1983-84 and 1986-87.
The Premier League's leading scorer delivered a brilliant second-half header that added to Sadio Mane's early strike and preceded Roberto Firmino's late goal.
Salah's goal, his 30th in the league, not only increased his advantage over Harry Kane in the Golden Boot race, but also strengthened Liverpool's grip on a top-four finish as they re-established their 10-point cushion over fifth-placed Chelsea.
The victory rounded off a fine week for Liverpool, who booked a Champions League semi-final against Roma by beating Manchester City 5-1 on aggregate with a second-leg win at the Etihad Stadium on Tuesday.
Reds boss Jurgen Klopp acknowledged on Friday that the forthcoming tie with Roma would be at the forefront of fans' minds, but his immediate priority of securing a top-four league finish was evident by the fact he made just one change to his team.
And four days after beating City his players backed up that attitude by flying out of the traps.
Salah could have scored in just the third minute, prodding a great opportunity wide from Trent Alexander-Arnold's whipped cross, but the first Reds goal arrived shortly after.
Jordan Henderson, the man Klopp had brought into the XI for James Milner, spotted Mane in the box and, although the Senegalese's header was saved by Asmir Begovic, the ball came back to him to stick away the rebound.
It continued to be one-way traffic in the opening 45 minutes and Begovic denied both Alexander-Arnold and Salah before Bournemouth finally threatened.
Yet even that attack was halted by the assistant's flag as Ryan Fraser was offside prior to collecting Charlie Daniels' back-heel and crossing for Jermain Defoe to tap home.
For all Liverpool's dominance, they only had one goal to show for it in the first half as Salah continued to be frustrated, with Steve Cook's brilliant challenge denying him.
There was a lack of intensity from both sides at the start of the second period, understandable given the early advantage Liverpool claimed and Bournemouth's position well clear of the relegation zone.
Salah certainly still had motivation in his battle to beat Kane to the golden boot, but there was a sense it might not be his day when he failed to win a penalty after a coming together with Nathan Ake.
Referee Chris Kavanagh was unmoved, but that ball over the top to Salah showed the way to get him in and he finally scored in the 69th minute.
Alexander-Arnold clipped a pass over Ake's head and on to Salah, who nodded superbly over Begovic and into the net for his 40th goal of a remarkable debut campaign with the Reds.
Mane and Firmino both came close to adding a third, while at the other end Dan Gosling fired at Loris Karius, but the only player in Liverpool's attacking triumvirate without a goal would find the target before the end.
Brazilian Firmino collected a pass inside the box from Alex Oxlade-Chamberlain, took a touch inside and then steered a shot through Simon Francis' legs and past Begovic's dive.