Eden Hazard's 25th-minute goal, struck low across Alisson, threatened to make him the Blues' match-winner against Liverpool for the second time in a week after his decisive strike in the 2-1 victory in the Carabao Cup at Anfield.
But the visitors wasted a host of opportunities and were facing their first league defeat of the season until substitute Sturridge curved a magnificent 25-yard left-foot drive high past Chelsea keeper Kepa Arrizabalaga with a minute of normal time left.
Jurgen Klopp's side fully merited their point, with the disappointing Mohamed Salah missing two chances and having a shot cleared off the line by Antonio Rudiger in the first half, before Xherdan Shaqiri missed an open goal and Roberto Firmino had a header swept off the line by David Luiz after the break.
Alisson also made crucial saves from Willian and Hazard as both teams remain unbeaten in the league but had to settle for a draw.
Why both managers can be happy...
Chelsea manager Maurizio Sarri and Liverpool counterpart Klopp smiled and embraced warmly at the final whistle of a high-class encounter that left them with mixed emotions.
Sarri will have been disappointed to see Chelsea concede so late but will have taken much pleasure from aspects of a performance that confirmed they have the qualities to remain in the race at the top of the Premier League this season.
With this result on the back of a 2-1 win at Anfield in the Carabao Cup in midweek, Sarri can look back on a highly satisfactory start to his Chelsea reign.
Klopp will feel the negative of the end of Liverpool's 100% start to the Premier League season - but he can reflect on a performance that resulted in so many chances created on opposing territory against a team they will rightly regard as close rivals in pursuit of the title.
He would have shaken his head in disbelief had Liverpool left Stamford Bridge empty-handed given the golden opportunities they let slip through their grasp. Liverpool, no matter how late they left it, deserved their point.
In the final reckoning, however, both Chelsea and Liverpool remain unbeaten with five and six league wins respectively - although the sight of Manchester City above them even after that superb opening is an ominous one.
Sturridge's spectacular late equaliser was another reminder that beneath the injury problems and the time on the sidelines lurks arguably England's most naturally gifted striker.
The last time he played at Stamford Bridge was on 12 January during a miserable loan spell with West Bromwich Albion. He limped off with a hamstring injury after only four minutes and did not play a full game for the rest of the season.
This was a different story.
Liverpool had tried just about everything and missed all manner of chances when Sturridge, with as much nonchalance as brilliance, looked up and sent a 25-yard finish in an arc past the stretching Kepa in the closing moments.
Sturridge combines athleticism and in-bred goalscoring instinct, as he proved with his bicycle kick in the midweek Carabao Cup tie against Chelsea, and would be a certainty for Gareth Southgate's England squad if he could string together a sequence of games.
As Sturridge walked off, taking the acclaim from Liverpool's fans, he cut a stark contrast with Salah, who did not last much longer than an hour against his former club and continues to struggle for form.
It is hardly crisis time for the Egyptian, who was never likely to repeat his 44-goal feat of last season, but he looks low on confidence at the moment - although he possesses such quality it is surely only a matter of time before he returns to his best.
Salah had three opportunities in the first half, with one finish weak and another wayward before he was denied by Rudiger's superb goalline clearance.
It simply was not his day, a fact accepted by Klopp as last term's talisman was removed and replaced by Shaqiri midway through the second half.
Hazard holds key to Chelsea's ambitions
Hazard, as he had at Anfield in midweek, threatened to be the difference between two very good teams as he punished Liverpool once more when he raced away and finished across Alisson in the first half.
He is, without argument, in the highest echelon of players in the world and his quality was reflected in the reaction of Klopp on several occasions when his side presented possession to the Belgian in dangerous positions.
Each time, Klopp clasped his hands to his Liverpool cap in a mixture of exasperation and anxiety, already well aware of the damage Hazard can do.
Put simply, if Hazard continues this form, Chelsea and Sarri have every chance of challenging for honours this season.
Man of the match - Eden Hazard (Chelsea)
A draw was right - what they said
Chelsea boss Maurizio Sarri: I am really happy with the performance. We are improving match by match. We played against a top level team and we played very well with quality and intensity.
"The draw is the right result."
Liverpool manager Jurgen Klopp: What a spectacular football game. We had chances and we played fantastic football. I love to win, but getting a point at Chelsea is good anyway.
"I know we deserved that point at least so I'm happy with that."
Liverpool strong at Stamford Bridge - the stats
- Chelsea have won only two of their past 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.
- Hazard is the Premier League's top scorer this season with six goals - he has scored those from just nine shots on target.
- Liverpool have only conceded two first-half goals in their past 13 Premier League matches - both at Stamford Bridge against Chelsea.
- 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).
- Sturridge has scored 17 Premier League goals as a substitute - only Olivier Giroud (19) and Jermain Defoe (24) have scored more.
- 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.
What's next?
Chelsea welcome Hungarian champions MOL Vidi to Stamford Bridge in the Europa League on Thursday (20:00 BST), then travel to Southampton in the Premier League on Sunday (14:15).
Liverpool visit Napoli in the Champions League on Wednesday (20:00) before welcoming Premier League champions Manchester City to Anfield on Sunday (16:30).
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