The Blues were denied a huge win at Stamford Bridge as substitute Daniel Sturridge scored an 89th-minute equaliser to cancel out Eden Hazard’s brilliant first-half opener.
An entertaining encounter ended with Chelsea and Liverpool sharing the points but for long spells it loooked as though we would take all three after Hazard had fired us into a 25th-minute lead.
It was a game in which there were chances at both ends and after the break Hazard, who could have made it 2-0, was denied by Alisson, before David Luiz cleared a Roberto Firmino header off the line.
The nature of Liverpool's leveller gives the result a disappointing feel to it but in truth, and on the balance of play, a draw is probably a fair result.
As expected, there were a number of changes to the side which started Wednesday's Carabao Cup game against the same opponents, with only Cesar Azpilicueta, Mateo Kovacic and Willian retaining their places.
Toni Rudiger, who went off injured at West Ham a week ago, came back into the starting line-up and Olivier Giroud was tasked with leading the line.
It was a lively opening to the contest as both teams looked to start on the front foot and the first opportunity fell the way of the visitors as Trent Alexander-Arnold’s ball deflected off N’Golo Kante and into the path of Mohamed Salah, whose low drive was comfortably saved by Kepa Arrizabalaga.
Salah should have done better a few minutes later when he got away from Rudiger on the edge of the Chelsea penalty area before slicing his strike high and wide, and Sadio Mane then blasted wide from a decent position after being teed up by Firmino.
The Blues were passing the ball well when we got forward but as the 20-minute mark approached Alisson in the Liverpool goal was yet to be tested.
That all changed when David Luiz picked out Willian with a superb pass out from the back, which the attacker did well to control with his first touch, before racing towards goal, only to be denied by Alisson, who had spotted the danger and raced off his line to make the save.
Four minutes later, and from our next attack, we were in front with a goal of the highest quality as Hazard, scorer of that stunning winner at Anfield three days ago, broke the deadlock.
The move started inside our own half, with Rudiger, Kante and David Luiz all involved. As it was played forward to the halfway line Hazard found Kovacic with a clever back-heel, and after exchanging passes with Jorginho the Croatian released Hazard with a superb pass. The Belgian still had plenty to do from a tight angle, but his early strike caught Alisson out and the ball fizzed past the keeper and into the far corner.
It was his seventh goal of the season and one which gave us a crucial advantage in the contest.
Liverpool looked to hit back immediately and David Luiz did well to head a dangerous Andrew Robertson delivery away, and his defensive partner Rudiger was even more impressive moments later when he raced back to clear a Salah strike off the line after the Egyptian had rounded Kepa having latched on to a Firmino ball.
The visitors worked themselves into a couple of dangerous positions as the half drew to a close, with Mane volleying acrobatically over the bar with the last of them, and as the teams heading in for the break Hazard’s goal was the difference.
Sarri’s side started the second half brightly and after Giroud had steered a Willian cross over the bar at the near post, Kovacic was thwarted as he looked to pull the trigger when Hazard’s teasing ball across goal had been cleared into his path.
Kepa then produced a superb save at the other end to deny Mane at his near post after the forward had wriggled away from a couple of challenges and got his shot away. The Spaniard got down quickly and tipped the strike around the post with a strong hand.
As we moved upfield Kante slipped Willian through but under pressure from both Van Dijk and Joe Gomez the Brazilian was unable to make the most of the opportunity and had to settle for a corner, which came to nothing.
A glorious opportunity presented itself moments later as David Luiz was tripped by Salah inside our half. The free-kick was taken quickly by Kante, who set Hazard free, but the Belgian's effort was saved by Alisson, with the ball bouncing up and over the top of the bar.
Around the midway point of the second half both teams made their first changes, with Alvaro Morata replacing Giroud for the Blues and Xherdan Shaqiri coming on for Salah for Liverpool.
The Liverpool sub was quickly into the action and should have equalised with his first touch as he arrived in front of goal to meet a Robertson delivery but somehow scuffed his shot wide.
The visitors continued to press for a leveller and it almost arrived from the head of Firmino, who powered a James Milner cross towards goal, only to be denied by his compatriot David Luiz who did brilliantly to divert the ball off the line.
Ross Barkley replaced the impressive Kovacic for the final 11 minutes and the departing midfielder received a fantastic ovation from the home fans in recognition of the overall quality of his display.
Kepa did well to hold on to a Shaqiri free-kick with seven minutes remaining and shortly afterwards Klopp made his final change by replacing Milner with Daniel Sturridge, and it was the substitute who secured a point for the visitors as he beat Kepa with a fierce drive from distance which flew into the top corner to make it 1-1.
The goal was timed at 89 minutes which told its own story.
However, our unbeaten start to the season continues and we can take heart from a fine display against strong opposition.
Attention now turns towards Thursday's Europa League home game against MOL Vidi, before we head to Southampton next Sunday in the Premier League.
Chelsea (4-3-3): Kepa; Azpilicueta (c), David Luiz, Rudiger, Alonso; Kante, Jorginho, Kovacic (Barkley 79); Willian (Moses 72), Giroud (Morata 64), Hazard.
Unused subs: Caballero, Cahill, Zappacosta, Fabregas
Scorer Hazard 25
Liverpool (4-3-3): Alisson; Alexander-Arnold, Gomez, Van Dijk, Robertson; Wijnaldum, Henderson (c) (Keita 77), Milner (Sturridge 85); Salah (Shaqiri 65), Firmino, Mane.
Unused subs: Mignolet, Matip, Moreno, Fabinho.
Scorer Sturridge 89
Booked Mane 38, Milner 76
Referee Andre Marriner