Mohamed Salah surpassed a long-standing Robbie Fowler achievement to fire Liverpool to a comfortable 3-0 win over Southampton.
Egypt international Salah struck twice in the space of 10 first-half minutes to put the hosts firmly in charge against the lacklustre Saints.
In doing so Salah, signed from Roma for a club-record fee in June, notched the ninth goal from his first 12 Premier League appearances on Merseyside, surpassing Liverpool’s previous best of eight from 12 set by Fowler in 1993.
The ex-Chelsea attacker’s exploits have helped to disguise the defensive failings of Jurgen Klopp’s side, although they were not at risk of being exposed by the toothless away team at Anfield on Saturday.
Coutinho, named in the side from kick-off after recovering from a thigh injury, set up Salah’s second and scored the third himself in a performance that demonstrated the continuing importance of a player targeted heavily by Barcelona in the off-season.
And the victory, Liverpool’s fourth in succession in all competitions, means they are just one point behind fourth-placed Champions League qualification rivals Spurs, who lost 2-0 at neighbours Arsenal earlier in the day, as Klopp’s attention turns to the crunch away match against Sevilla on Tuesday.
The visitors almost gifted Liverpool the lead in the ninth minute as Virgil van Dijk’s mistake, Cedric Soares’ missed clearance and a Fraser Forster fumble saw the ball fall to Salah, but the Egypt international’s shot was deflected wide.
Another error prompted Liverpool’s opener to arrive in the 31st minute, and this time Dusan Tadic was to blame, the Serbia international losing possession after attempting to dribble the ball clear following a corner.
A quick exchange of passes after the turnover saw Georginio Wijnaldum tee up Salah, who curled a brilliant strike into the top left corner from 20 yards.
Southampton’s defence were found badly wanting for the second goal 10 minutes later.
Coutinho glided forward unopposed and prodded a clever pass into the area, which Salah raced on to and slid between the legs of the helpless Forster.
Southampton enjoyed a rare sight of goal six minutes into the second half, Sofiane Boufal cutting into the area from the left, but seeing his shot blocked by the massed ranks of the Liverpool defence.
Coutinho went close four minutes later, dribbling directly at goal and shooting narrowly wide with Forster scrambling.
The England international shot-stopper was left with no chance five minutes later. He did well to parry a fierce Roberto Firmino strike from a tight angle on the right side of the penalty area, but the rebound fell kindly to Coutinho, who steered home a cool finish to put the result beyond any doubt.
In other Premier League results:
Crystal Palace missed the chance to pick up three precious points as the Premier League’s bottom club were twice pegged back by Everton in an entertaining 2-2 draw at Selhurst Park.
Callum Wilson netted a superb hat-trick to help 10-man Bournemouth move clear of the Premier League relegation zone with a convincing 4-0 win over Huddersfield Town.
Jack Cork inspired Burnley to a 2-0 win against former side Swansea City on Saturday, earning his new employers a third straight top-flight victory for the first time in the Premier League era.
Eden Hazard and Alvaro Morata ran riot as Chelsea outclassed West Bromwich Albion 4-0 at the Hawthorns to turn up the heat on Tony Pulis.
Pep Guardiola’s rampant Manchester City made it 10 Premier League wins in a row with a typically dominant 2-0 victory over Leicester City.