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.
helsea 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.
Liverpool will be thrilled to have avoided defeat, especially given the games to come next week: a trip to Napoli in the Champions League, and a showdown with City at Anfield.
