The Reds, who made eight changes to their starting line-up for the contest, took an early second-half lead through Daniel Sturridge’s well-executed finish after Willy Caballero had saved from Naby Keita.
However, late efforts from Emerson and Eden Hazard ensured it will be Maurizio Sarri's men in Saturday’s draw for the next stage of the competition.
Here are five talking points from the game…
A first defeat…
After winning each of their seven opening games of 2018-19 in all competitions, setting a new club record in the process, Liverpool have suffered a first loss of the campaign.
It’s the first reversal for the Reds at Anfield since being defeated by West Bromwich Albion in the FA Cup fourth round on January 27 of this year.
A goal a home game for Studge…
Sturridge has made three appearances at Anfield this season – and scored in each of them.
He needed a mere matter of seconds to find the back of the net after coming on as a substitute against West Ham United on the opening day of the campaign and then headed in the crucial opener against Paris Saint-Germain last week.
Tonight’s strike was probably the pick of the bunch as he demonstrated his killer instinct to react to Caballero’s save from Keita by smashing a scissor-kick home to break the deadlock.
It was the second goal Sturridge has bagged for Liverpool against his former employers – the previous one also coming at the Kop end back in April 2013.
A debut and a comeback…
Tonight provided a first start for Liverpool for Fabinho following his summer transfer from AS Monaco.
Competitively, the No.3 had only figured as a late substitute versus PSG prior to tonight.
Meanwhile, after an outstanding World Cup campaign with Croatia, in which they defied the odds to reach the final against France, Dejan Lovren registered a maiden appearance of the campaign.
The centre-back had been nursing a pelvis injury since returning to Melwood in August, but was back in the Reds’ starting XI for the first time since May, partnering Joel Matip in the middle of the back four.
A video assistant…
VAR was in use at Anfield for only the second time - and was called into play to check whether there was an offside when Emerson tucked in Chelsea’s equaliser from a free-kick after Simon Mignolet had stopped Ross Barkley's header at a free-kick.
After a brief delay, it ruled in favour of the visiting defender and the goal was awarded to level up the scoreline at 1-1.
A chance to respond…
Liverpool won’t have to wait long for a chance to attempt to strike back against Chelsea – the teams meet again on Saturday evening.
The two will go head-to-head in a Premier League clash at Stamford Bridge, with the Reds holding a two-point lead over the Blues after six games.