Liverpool showed Chelsea still have far to go to challenge the champions for the Premier League title as Sadio Mane took advantage of a first-half red card shown to Andreas Christensen to score both goals in a 2-0 win at Stamford Bridge.

Mane provoked the Dane's dismissal and then headed the Reds into the lead before pouncing on another terrible error from the Blues' goalkeeper Kepa Arrizabalaga.

At the other end, Alisson Becker also proved the value of a good goalkeeper as he saved Jorginho's penalty 15 minutes from time to deny the Blues a lifeline.

Victory takes Liverpool level on points with Everton, Arsenal and Crystal Palace at the top of the table as the only sides with maximum points from their opening two games.

Chelsea have spent 200 million ($260 million) in the transfer market to try and close the 33-point gap between the sides last season, but the decision to invest most of that in forwards rather than addressing more urgent defensive needs was badly exposed.

A lack of defensive reinforcements with Thiago Silva still not match fit was obvious in Frank Lampard's gameplan as the Chelsea boss tried to protect a backline that conceded 54 league goals last season in a cagey first-half.

Christensen bailed out Kepa from another embarrassing error as he was caught in no man's land early on but the defender got back to prevent Roberto Firmino converting Mohamed Salah's cross.

Despite Liverpool dominating possession, Chelsea had the best sight of goal in the first half when Timo Werner dragged wide from the edge of the box.

But the hosts' good defensive work was undone seconds before the break as Mane raced onto Jordan Henderson's ball over the ball and was hauled down by Christensen.

Referee Paul Tierney initially only showed a yellow card, but overturned his decision after viewing the incident on a pitchside monitor and Christensen was dismissed.

Jurgen Klopp irked Lampard when he said the Reds could not behave like clubs owned by oil-rich states or oligarchs such as Manchester City and Chelsea in the transfer market.

But Liverpool have been busy this week with Thiago Alcantara and Diogo Jota becoming their first major signings for two years.

Klopp instantly called for Thiago to make his debut at half-time in place of the injured Henderson and it took just five minutes in the second-half to make the breakthrough.

Mane again did the damage as he met Firmino's cross with a firm header into the far corner.

Chelsea's spending spree is not yet over with Edouard Mendy set to join from Rennes as Lampard's patience with Kepa, who cost a world record 72 million for a goalkeeper two years ago, exhausted.

Liverpool's second will only have confirmed the former England midfielder's decision as Kepa's casual pass was intercepted by Mane, who then turned the ball into an empty net.

Alisson's record as the world's most expensive goalkeeper lasted just three weeks in 2018 between his move from Roma and Chelsea paying Kepa's buyout clause from Athletic Bilbao.

But the Brazilian has more than justified his 67 million price tag in wining the Champions League and Premier League over the past two seasons and produced a big save when Liverpool needed it.

Thiago did not have a dream debut as he was the culprit for clipping Werner's legs as he burst into the area.

Jorginho's stutter-step run up has fooled many a goalkeeper in the past, but Alisson held his ground before diving low to his left to save.