Summer signing Alexis Mac Allister was sent off in his first home match for Liverpool but the Reds still overpowered Bournemouth in a thrilling Premier League game at Anfield.

The Cherries, who had already had a goal disallowed because Jaidon Anthony was offside, scored inside three minutes when the Reds gave away possession and Antoine Semenyo fired sweetly into the bottom corner.

Jurgen Klopp’s side eventually got into their stride in a frantic first half and scored twice in an eight-minute period.

Luis Diaz got the equaliser when he collected Diogo Jota’s low cross, flicked the ball up, spun and volleyed home.

Summer signing Dominik Szoboszlai then went to ground after a challenge at the corner of the box by Joe Rothwell and Mohamed Salah converted the rebound after his penalty was parried by Bournemouth goalkeeper Neto.

Argentina World Cup winner Mac Allister, signed in a £35m deal from Brighton, was shown a straight red card midway through the second half when he caught the foot of Ryan Christie.

But the 10 men of Liverpool scored a third as Szoboszlai’s low shot was pushed out by Neto and Jota netted from close range.

The win means Liverpool now have four points from two matches this season after they began with a 1-1 draw at Chelsea while Bournemouth have just one point from their opening two games.

Both managers may be unhappy with refereeing decisions from Thomas Bramall, with Liverpool’s penalty appearing a soft decision as Rothwell made minimal contact with Hungary captain Szoboszlai as he stretched out his leg.

Klopp will be disappointed with the decision to send off Mac Allister for what seemed a genuine attempt to win the ball.

While there did not look to be any malice in the challenge, the former Brighton midfielder’s boot was high as he caught Christie.

The Liverpool fans booed the decision while Klopp tried to provide some words of comfort for the Argentine as he walked off the pitch after an inauspicious end to his Anfield debut.

This summer saw Liverpool lose captain Jordan Henderson and fellow midfielder Fabinho to Saudi Arabian clubs on top of James Milner, Roberto Firmino, Naby Keita and Alex Oxlade-Chamberlain leaving on free transfers.

They have completed deals for Mac Allister, Szoboszlai – in a £60m transfer from RB Leipzig – and Japan midfielder Wataru Endo, who moved in a £19m deal from Stuttgart on Friday and looked neat and tidy when he came on in the second half after the Argentine’s dismissal.

However, two of Klopp’s key midfield targets – Moises Caicedo and Romeo Lavia – have chosen to join Chelsea from Brighton and Southampton respectively, leaving Klopp light on central midfielders.

Nevertheless, Liverpool have four points from their opening two matches and their excellent run at Anfield continued – they have now gone 13 Premier League matches since they lost at home, when Leeds United beat them in October 2022.

Bournemouth were a lively presence if a little open and Liverpool threatened to run away with the match after the Diaz and Salah goals settled them down.

Trent Alexander-Arnold, on his 200th Premier League appearance, had a shot saved while new captain Virgil van Dijk headed wide and the impressive Szoboszlai saw an effort deflected off-target.

That pressure was maintained at the start of the second half as Jota shot wide when Neto had headed outside of his penalty area, and Salah fired at the goalkeeper from a tight angle.

Mac Allister’s red card in the 58th minute threatened to change the direction of the match and give Bournemouth hope of winning at Anfield for the first time.

However, the south coast side’s hopes were quickly dashed four minutes later when Jota pounced after Neto could not gather Szoboszlai’s strike.

Despite a late flurry from the visitors that saw Alisson make fine saves to deny substitutes Justin Kluivert and Hamed Traore, Liverpool claimed a deserved three points.