Mo Salah was put through by Trent Alexander-Arnold in the 20th minute to score the opener and his 100th Premier League goal. The Reds continued to make chances but they couldn’t convert them and headed into the break 1-0 up.
In the second half a corner, earned by Sadio Mane and Salah, ended in Fabinho doubling their lead as he took a touch, smashed it home and it stood after a VAR check.
Leeds then went down to 10 men as Harvey Elliott was injured in a heavy challenge, stretchered off the pitch as Pascal Struijk was given a red card.
Mane added their third in stoppage time, a deserved and overdue strike after having 10 chances in front of goal.
Here are five things we learned from the game on Sunday.
Mo Salah continues to be Reds’ leading man
Mo Salah was everywhere for Liverpool in the opening 10 minutes, even managing to throw off Kalvin Phillips.
He put Diogo Jota in for a great chance at 14 minutes, with keeper Illan Meslier having to make a great save to stop the Reds from scoring. Salah kept pushing for an opener and it came in the 20th minute, his 100th Premier League goal - 98 for the Reds, two for Chelsea - thanks to a clean pass from Trent Alexander-Arnold.
Salah kept dominating on the pitch and was a nuisance for the hosts in the second half.
He almost had a second in the 47th but played a part in earning a corner. The set-piece resulted in the second goal.
The Egyptian international attracted transfer rumours in the summer and the Reds will need to stave off future offers as he is pulling all the strings at the moment.
Struijk shown red for heavy challenge
Struijk challenged Elliott, who was about to be subbed off for Jordan Henderson, and the 18-year-old remained on the ground after clutching his ankle. Medical staff rushed onto the pitch and surrounded the youngster in a heart-breaking moment for Liverpool.
Struijk left the field and headed straight for the tunnel, visibly upset. Elliott did manage to applaud fans as he left the pitch on a stretcher.
It was later confirmed the decision to send off the midfielder would have been taken regardless of how brutal the injury was.
The dismal timing of Elliott’s absence comes as he was making his breakthrough in the Reds’ team, having earned a starting role in midfield this season.
Leeds defence needs calming influence
The hosts play in a high tempo fashion but the defence in the first half felt forced and desperate. They started steady but cracks began to show before they conceded the first goal.
Liam Cooper was booked for pulling Mane to the floor which gifted Liverpool a free kick. Luckily for the skipper, the opportunity was wasted by the visitors.
Leeds are unable to gain consistency in their back line, which they desperately need, due to the re-occurring injuries of Diego Llorente, who limped off with a hamstring problem in the first half.
There were glimpses of cohesion as Luke Ayling stopped the Reds from scoring with pressure on Mane, which made the star miss an easy shot in front of an open goal.
Harrison has potential to unlock Leeds’ season
Jack Harrison has created the most chances in the Premier League so far this season and he carried on his fabulous form in those terms.
He danced his way through two defenders on the edge of the box to feed his teammates but Junior Firpo’s shot was blocked.
Just before the break Harrison fed another ball into the box in only Leeds’ second decent spell of possession. If he keeps up his great form his team will catch up with him and slot home all the chances he is creating.
Liverpool need to do more to worry rivals
Jurgen Klopp’s side secured three points and a clean sheet in the fixture but the amount of wasted chances doesn’t yet put fear into their rivals.
They need to be more clinical, especially with the results and performances seen by the likes of Chelsea this weekend. No clear top five have emerged just yet but if the Reds’ final third touches were cleaner they could have topped the table alone on goal difference.
Liverpool displayed all the aspects of their game that shine in the match but if they get a consistent 90 minutes together they will leave many teams for dust.
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