Sadio Mane opened the scoring after just three minutes but after Virgil van Dijk was withdrawn following a collision with Jordan Pickford, Michael Keane capitalised to equalise from a corner.
Liverpool finally retook the lead after 72 minutes as Mohamed Salah scored a brilliant rebound, only for Everton to respond again as Calvert-Lewin’s towering header converted James Rodriguez’s cross.
The final 10 minutes descended into chaos as Richarlison was red carded for a rash challenge on Thiago, while Jordan Henderson’s would-be winner was ruled out by VAR in what seemed the narrowest of offside decision.
Here are our player ratings:
Jordan Pickford: 6 out of 10 – Made a couple of good saves to deny Trent Alexander-Arnold in first half and Joel Matip in the second but was lucky to still be on the pitch after an awful challenge on Virgil van Dijk.
Seamus Coleman: 3 out of 10 – Got beaten repeatedly by Andy Robertson which led to the opening goal and then pulled a hamstring and had to go off after 30 minutes. A game to forget for Everton’s captain.
Michael Keane: 7 out of 10 – Scored Everton’s first equaliser with a decent header from a corner. Provided a strong presence in both penalty areas from set pieces.
Yerry Mina: 6 out of 10 – Was a threat when up the pitch winning most of the balls sent into him but made an error trying to clear the ball in the second half and allowed Salah to score.
Lucas Digne: 8 out of 10 – Had a good game at the back making some crucial tackles and clearances. Also got forward and provided some decent crosses into the box, including a beautiful pass to Dominic Calvert-Lewin for Everton’s second.
Allan: 6 out of 10 – Struggled to get on the ball in the first half as Liverpool won the midfield battle, did better in the second and got stuck in.
Abdoulaye Doucoure: 5 out of 10 – Got overshadowed in midfield and didn’t have the same kind of impact he’s been enjoying for Everton this season.
Andre Gomes: 6 out of 10 – Provided a few decent passes and tracked back well. Worked hard for little reward.
James Rodriguez: 8 out of 10 – Delivered the cross to Keane that got Everton back on level terms and played some beautiful balls up to Richarlison and Calvert-Lewin.
Richarlison: 5 out of 10 – Was slow to get into the game and looked off his best. Hit the post in the second half when he should have scored before getting sent off five minutes before the end of the match.
Dominic Calvert-Lewin: 8 out of 10 – A quiet game by his recent standards. Had a couple of good chances; a header that went over and a shot from the right saved by Adrian before finally scoring and earning Everton a point.
Adrian: 6 out of 10 – Made some decent saves to deny Calvert-Lewin and Gomes but could have done better to stop Keane’s header. Still looks a little shaky but it was a better performance from Liverpool’s goalkeeper.
Trent Alexander-Arnold: 6 out of 10 – Had a curling shot denied by Pickford in the first half and delivered some decent crosses into the box.
Joel Matip: 6 out of 10 – Had to step up at the back after van Dijk was subbed off and did okay against Calvert-Lewin. Impressed on his first game back from injury.
Virgil van Dijk: 5 out of 10 – Was a commanding presence for the small amount of time he was on the pitch. Got taken out by Pickford and left a big hole in Liverpool’s defence.
Andy Robertson: 8 out of 10 – Had the beating of Coleman on the left wing and combined with Mane effortlessly. Got one assist, should have had more.
Fabinho: 6 out of 10 – A solid day out for the midfielder who controlled the ball in the middle of the pitch and let the players with more flair take the headlines.
Thiago Silva: 7 out of 10 – Looked desperate to make a positive impact on his first Liverpool start and showed signs of his creativity around the box and got stuck into the physicality of the game in midfield.
Jordan Henderson: 7 out of 10 – A stable presence in Liverpool’s midfield, encouraging them to go forward. Sent a decent cross into the box to lead to Salah’s goal.
Sadio Mane: 8 out of 10 – Looked hungry for goals after missing the Villa game before the international break, opened the scoring with a clinical shot and provided an ever-threatening partnership with Robertson on the left wing.
Roberto Firmino: 5 out of 10 – Linked up with Salah and Mane a couple of times in and around the box but didn’t do much else.
Mo Salah: 7 out of 10 – Had a quiet game but still got on the scoresheet by turning up in the right place at the right time. Brilliant finish to score Liverpool’s second.