A superb strike from Mason Mount was all that separated both sides at Anfield, but it was enough to condemn Liverpool to a fifth-straight home defeat.
Chelsea thought they opened the scoring earlier in the game. Timo Werner used his electrifying pace to outrun Fabinho before beating Alisson and tapping the ball into an empty net. But VAR ruled the goal out, as the German was adjudged to have strayed inches offside in the build-up.
The visitors continued to probe and finally clinched the opener when Mason Mount dazzled into the Liverpool box and drilling a powerful strike into the bottom corner to give his team the lead going into the break.
With Liverpool posing no threat in attack in the second half, Chelsea came close to a second when Hakim Ziyech whipped in a beautiful cross for the outstretching Timo Werner.
Liverpool continued to offer nothing in attack, and Chelsea were all too happy to see out the win.
The Blues are now unbeaten in ten games since Thomas Tuchel in all competitions, a superb run that includes games with Atletico Madrid, Manchester United and Liverpool.
On that note, let's take a look at the player ratings of both teams.
Liverpool player ratings against Chelsea
Returning to the fold for the first time since the death of his father, the Brazilian shot-stopper had a shaky start to the game.
Liverpool were lucky to be still on level terms midway through the game, as Alison was beaten by the onrushing Timo Werner, who tapped the ball into an empty net. However, the goal was chalked off for offside.
The Liverpool keeper did make a brilliant stop to deny the German in the second half, but there was nothing he could do about Mason Mount's fine finish.
Trent Alexander-Arnold 6/10
He was targetted by the Chelsea attack, who kept pinging balls over the top towards Timo Werner.
Trent-Alexander Arnold was easily beaten by Mason Mount for Chelsea's opener. Despite trying to make something happen for Liverpool in attack, he was met by a resilient Chelsea defence.
Fabinho was also making a return to the fold following an injury spell. However, he looked to struggle with fitness the entire game and was often cut out by Chelsea's passes over the top. Fabinho was in no-man's-land for Chelsea’s opener and looked off-pace for most of the game.
Ozan Kabak 6/10
It was not the most assured performance from the former Schalke man. While Ozan Kabak was easily the best of Liverpool’s centre-back pair, he struggled to play out from the back against Chelsea’s high press.
Andy Robertson 5.5/10
Andy Robertson failed to contribute anything meaningful on the night, as Chelsea pegged him back in his half for most of the game. However, when Robertson pushed forward, he struggled to link up with Sadio Mane, failing to make any telling contribution in attack.
Georginio Wijnaldum 6.5/10
A solid presence at the centre or the park against Chelsea, Georginio Wijnaldum kept the ball alive in midfield. He lined his defence and attack brilliantly and was solid on the ball as he bounced off the Chelsea press with ease. However, Wijnaldum was let down by his teammates.
Thiago Alcantara 5/10
Thiago Alcantara was simply outplayed and outclassed by Chelsea’s midfield genius, as he once again struggled to lay a foothold on the game. The Spaniard fizzled out of the game and was eventually replaced by James Milner.
Curtis Jones 5/10
Curtis Jones was Liverpool's hero in the win over Sheffield United, but he failed to replicate that performance against an inspired Chelsea side. He was tidy with his passes, completing over 95% of them, while winning three ground duels before he was replaced by Diogo Jota at the hour mark.
Mohamed Salah 5/10
Mohamed Salah continues to look a shadow of his former self since the turn of the year, as he failed to hit his stride against Chelsea. He was bamboozled by the Blues defence, particularly Antonio Rudiger, and struggled to string threatening plays in attack. To his annoyance, he was hooked off after just 62 minutes for Alex-Oxlade Chamberlain.
Sadio Mane 6/10
The Senegalese posed a threat to the Chelsea defence. But he lacked the cutting edge to turn it into something meaningful, as he came second best against Cesar Azpilicueta more often than not.
Roberto Firmino 5/10
Another toothless outing from Liverpool’s Brazilian striker. He was given the nod ahead of the returning Diogo Jota, but he offered no threat in attack.
Player ratings of Liverpool substitutes
Alex Oxlade-Chamberlain 5/10
The Englishman made little or no impact after replacing Mohamed Salah, making Jurgen Klopp's decision questionable.
Diogo Jota 6/10
Diogo Jota came on for Curtis Jones in the 62nd minute and injected life into the Liverpool attack. His silky movement often had the Chelsea defence on its toes, but he never really looked like grabbing the all-important equaliser.
James Milner 5/10
James Milner came on for the final minutes of the game but was merely a spectator.