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Fulham got back in front when Jarell Quansah should have been stronger against Robinson before he was allowed to cut the ball back to Rodrigo Muniz.
Slot responded by introducing Diogo Jota three minutes later, and it was the Portugal international who equalised with a well-placed finish past Bernd Leno.
A performance that the Reds can take positives from.
Andrew Robertson was sent off after just 17 minutes. Alex Livesey/Getty ImagesNegatives
Chance creation in the first half had to be better, though the red card meant that Slot didn't have time until the break to properly tweak his system.
Manager rating (1-10; 10 = best)
Arne Slot, 9 -- Slot's side never lost control of the game despite going down to 10, and there were clear signs of a gameplan in the second half as Liverpool began to create a regular flow of chances.
There was little Alisson could have done about either goal he conceded.
DF Andrew Robertson 1 -- Seventeen minutes to forget for the Liverpool left-back saw him take a heavy challenge from Issa Diop early on, help Pereira's effort past Alisson, and then get sent off for a foul on Harry Wilson as the last defender.
DF Virgil van Dijk 7 -- Assured at the back and impressed with transitioning the ball into midfield areas to help Liverpool overcome the numbers advantage.
Deployed in a midfield role later on in the match and helped Liverpool maintain control following the introduction of Darwin Núñez saw the Reds change shape.
MF Ryan Gravenberch 7 -- Deployed at centre-back when Liverpool went down to 10 and linked well with Van Dijk to help move past Fulham's initial press.
Booked for an over-zealous challenge on Alex Iwobi.
MF Dominik Szoboszlai 8 -- A standout for Liverpool on the day, impressing with both his work-rate to assist defensively and decision-making in the final third, where he utilised his pace to break into space before unlocking the game for the forward line.
FW Cody Gakpo 7 -- Got Liverpool back on level terms by connecting with Mohamed Salah's cross, and showed his intelligence during counter-attacks, holding up the ball to bring others into play and choosing the right moments to challenge defenders directly.
FW Luis Díaz 5 -- Booked harshly for an innocuous overhead kick attempt, but faded out of the game when Liverpool went down to 10, outside of a chance with a header that he should have done better with.
Should have hit his effort first time in the 94th minute.
FW Mohamed Salah 7 -- Consistently enjoyed the better of the duels against Robinson and was an out ball for Liverpool by keeping wide on the right-flank.