Jurgen Klopp's side looked to be heading for a second defeat to the Blues this week after Eden Hazard struck a brilliant opener, but Sturridge's emphatic effort from distance in the 89th minute rescued a point.
The draw, which comes just three days after Chelsea claimed a 2-1 EFL Cup win at Anfield, means Liverpool's 100 per cent winning record in the Premier League this season ends and they are level on points with leaders Manchester City, behind only on goal difference.
Chelsea sit two points further back after a thrilling encounter, but, like Liverpool, remain unbeaten.
Mohamed Salah wasted two early half-chances before Willian was thwarted by Alisson, but Liverpool fell behind for the first time in the league this season 25 minutes in through a stunning Hazard goal.
The Belgium star combined with Olivier Giroud and Mateo Kovacic in the centre-circle, raced onto the midfielder's pass and rifled the ball across Alisson and into the bottom-right corner.
Salah looked to have levelled 32 minutes in after escaping Marcos Alonso and rounding Kepa Arrizabalaga, but the covering Antonio Rudiger stretched to clear the ball off the line.
Kepa denied Sadio Mane with a strong reflex stop in the second half, but Chelsea looked a threat on the break and Alisson denied Hazard one-on-one after a quick free-kick.
The disappointing Salah was replaced by Xherdan Shaqiri as Liverpool chased their equaliser, and the Switzerland international promptly side-footed wide with the goal gaping after Andy Robertson had capitalised on Alonso's slip.
Roberto Firmino saw a header hooked off the line by David Luiz as the visitors kept Chelsea pinned back, before Sturridge rescued a result with a curling strike from nearly 30 yards out that left Kepa with no chance.
What it means: Liverpool lose perfect record as well as top spot
Liverpool were the last team to have a 100 per cent record in the top flight this season before Saturday, but they now sit behind Manchester City, who saw off Brighton and Hove Albion 2-0 earlier on Saturday, on goal difference.
Maurizio Sarri will likely be the more disappointed given the time on the clock when Sturridge struck, but an EFL Cup win and Premier League draw with Liverpool in the space of three days is certainly no mean feat.
Hazard leaving the Premier League in his wake
Hazard's winner at Anfield this week was a goal that will not quickly be forgotten, but his strike on Saturday deserves almost as many plaudits given the team move that preceded it.
It was a slick piece of play started and finished by Hazard and underlined the confidence and flair with which he is playing at present. Questions about being the best in the world are best saved for another time, but he is certainly the in-form man in England's top flight.
Salah still missing his X-factor
Salah was always likely to have his form scrutinised more closely this season given his stunning exploits in 2017-18, and this performance will have done little to keep the critics off his back.
He missed two decent half-chances in the first half before seeing Rudiger deny him in athletic style, and his link-up play with Roberto Firmino was a long way short of its brilliant best. He was taken off for Shaqiri with 24 minutes left.
Key Opta stats:
- Chelsea have won only two of their last nine home Premier League games against Liverpool (W2 D3 L4).
- Liverpool remain unbeaten in their opening seven matches of a Premier League season for the first time since 2008-09.
- Chelsea's Eden Hazard is the Premier League's top scorer this season with six goals – he has scored those six goals from just nine shots on target.
- This was the 38th home Premier League game that Hazard has scored in – he has never ended on the losing side in any of those games (W34 D4 L0).
- Liverpool's Daniel Sturridge has scored 17 Premier League goals as a sub – only Olivier Giroud (19) and Jermain Defoe (24) have scored more off the bench in the history of the competition.
- Daniel Sturridge is the seventh player to score 50 Premier League goals for Liverpool, after Robbie Fowler, Steven Gerrard, Michael Owen, Luis Suarez, Fernando Torres and Dirk Kuyt.
Liverpool face a difficult test when they visit Napoli in the Champions League on Wednesday, and it does not get much easier at the end of the week, when champions and new leaders Manchester City travel to Anfield.