Jurgen Klopp’s side extended their best start to the title race as they became the first team to win their opening six matches in successive top-flight seasons.
Alexander-Arnold’s blistering free-kick opened the scoring in Stamford Bridge.
Roberto Firmino raised Liverpool’s benefit before the period, and N’Golo Kante’s attractive target wasn’t sufficient to provide Chelsea real reward for a lively second half.
Following Manchester City thrashed Watford 8-0 on Saturday this was the perfect answer from Liverpool as they bid to acquire the title for the first time since 1990.
Pipped to the decoration from City on the last day of last year, Liverpool is playing a burning desire to finish their opponents’ two-year reign as winners.
Compared to the Champions League holders’ scrappy midweek defeat Napoli, this disciplined screen revealed the Premier League is Liverpool’s highest priority that term.
Notably because of their name prospects, Liverpool’s success in the Bridge was only their second win in 13 away league matches against another based top-six teams.
Though they had been hanging by the conclusion, if Liverpool takes more things from the big guns, even City would struggle to maintain them at bay.
Frank Lampard’s uncooked facet, 10 points behind the leaders, competed gamely to provide hope of a bright future.
A frenzied beginning might have attracted a Chelsea opener when Tammy Abraham extended in a vain effort to flip into Mason Mount’s teasing cross.
Those two Chelsea kids have caught the eye at the beginning of Lampard’s reign.
However, it was Liverpool who took the lead from the 14th minute thanks to his very own talented prodigy.
Fabinho’s pass broke to Sadio Mane along with the Liverpool winger was sprinkled to the edge of the playground by Andreas Christensen’s clumsy challenge.
Mohamed Salah back-heeled that the free-kick to the route of Alexander-Arnold along with also the 20-year-old right-back smashed a sublime shot beyond Kepa Arrizabalaga to the upper corner for his first goal since November 2018.
Abraham has scored seven Premier League aims. However, the striker fluffed his lines when he overcomes the Liverpool offside trap to fulfil Christensen’s long pass.
Chelsea thought they had equalised from the 27th minute when Cesar Azpilicueta prodded home from close range after Willian’s cross diverted into the protector off Fabinho.
However, in a massive momentum swing, the goal was disallowed following a VAR review revealed Mount was offside from the build-up.
Lampard wore a rueful grin on the touchline and, minutes later, the Chelsea manager’s saying was distress personified as Liverpool doubled their lead in the 30th minute.
Andrew Robertson curled upwards of a free-kick in the left border of the Chelsea area and Firmino, talented far too much distance from Christensen and Marcos Alonso, climbed highest to head his third objective of the season.
Kepa made an excellent save to prevent Firmino placing Liverpool farther ahead from Alexander-Arnold’s cross in the second half.
However, Chelsea’s effort could not be faulted and, with harried Liverpool on the trunk, they decreased the deficit at the 71st minute.
Kante turned off from Fabinho using a graceful glide and, with Liverpool sitting sincerely, the France midfielder curled a great strike into the top corner.
Michy Batshuayi was inches from equalising from the last moments, but Liverpool held on.