Eden Hazard continued his excellent start to the season, but the reds were deservedly rescued by a late Sturridge stunner.
Sturridge and Hazard were both on the scoresheet in the League Cup 3rd round game on Wednesday, on that occasion Hazard striking the winner to knock the reds out of the cup.
But here Sturridge came off the bench to become joint top LFC scorer this season, despite only playing around 180 minutes.
A point was the minimum deserved by the reds who had plenty of chances throughout the game.
Mo Salah was withdrawn mid-way through the second half after more disappointment in front of goal.
Both Salah and Firmino did have chances cleared off the line during the game.
The reds slip a place to second after the weekend, level on points with Man City but with an inferior goal difference.
However, a point at Stamford Bridge is one more than they managed last season, and the manner in which it was eventually secured could prove important as the season wears on.
Eden Hazard had opened the scoring slap bang in the middle of the first half when he powered clear of the Liverpool defenders to score a seventh goal of the season.
Sturridge arrived on for the final four minutes of the game and within three minutes unleashed his rocketing shot that beat the £71M Kepa Arrizabalaga in the Chelsea goal.
For his part, the Liverpool boss was pleased for Sturridge.
"It was so deserved for Daniel , a really nice moment and I'm so happy for him.
"I think we made one mistake in the game leading to their goal. It's difficult. We had chances, we played fantastic football. I love to win, but getting a point at Chelsea is good anyway. You can see how good Chelsea are but its nice to see it again.
"I know we deserved that point at least so I'm happy with that."
Liverpool's attention now turns back towards the Champions League as they prepare to face Napoli in their second group game.