The England international found the net in the 88th minute to snatch Liverpool a point after Chelsea failed to kill the game off.
Were it not for Sturridge's peice of magic the main story would have been Hazard scoring his sixth Premier League goal of the season to give Chelsea all three points. However it was not to be for Mauricio Sarri's side, with Liverpool's number 15 coming back to haunt his former side only 3 minutes after coming off the bench for Milner.
Both teams looked dangerous throughout the fast paced encounter, with a draw proving to be a fair reflection of the game, but if the 'blues' had closed the game out, Liverpool could not have complained.
The Merseyside team started the brighter of the two title challengers, but Mohammed Salah could not find his customary end product after doing well to create openings on a few occasions.
However Chelsea grew into the game and Willian was denied one on one before their Belgian superstar Hazard gave them the lead in the 25th minute. The build up in midfield was typical of the famed 'Sarri-ball' that their manager is so famous for, fantastic interplay freed Mateo Kovacic between the lines and the loan signing from Real Madrid found Hazard with a great forward pass.
It looked like he might have taken the ball slightly too wide, but he finished low and hard across Alisson on his weaker left foot to put Chelsea ahead.The Liverpool goalkeeper, who was excellent throughout, may have been slightly disappointed that he didn't get down to his left more quickly to maintain his clean sheet.
Six minutes later Liverpool could have been level, but Salah's uncharacteristic day continued. Racing through on Kepa he took the ball around the young 'keeper but gave Antonio Rudiger enough time to get back on the line and smash his low shot ot safety.
Chelsea, however made it to half time unscathed, with Sadio Mane's acrobatic effort not coming close to threatening their goal.
The second half looked to have calmed down a bit, but Kepa saved again in the 58th minute, turning Mane's low shot on the spin around his post.
Within five minutes Hazard could have killed the game for Chelsa. He was put in the clear and with the form he's in it looked for all the world like it would be 2-0. Alisson, however, had other ideas, pulling off his second save one against one in the match.
No doubt boosted by this, the momentum in the game started to change and Liverpool really should have been level in the 70th minute.
Xherdan Shaqiri, recently on for the misfiring Salah had a golden chance to equalize. Andy Robertson's low cross found the summer signing in acres of space 10 yards out, but his right footed effort went inches wider of Kepa's post.
From here on it looked like Chelsea would survive and inflict Liverpool's first defeat of the season. However their former striker Sturridge had other ideas.
He came on for James Milner in the 86th minute and within three minutes he had made his mark.
Sturridge is no stranger to spectacular strikes, but few of his 49 other Premier League goals for Liverpool match up to this one. He picked up the ball so far out that N'golo Kante didn't even seem like it was necessary to close him down. A big mistake. The resurgent star wound up a phenomenal curling and dipping efford that span away from Kepa and into the top corner, in a cruel twist of fate for the outstanding shot stopper.
David Luiz and Antonio Rudiger also put in stellar performances at the back, but it was not enough to deny Liverpool, who snatched a draw from the jaws of defeat, which saw both teams maintain their unbeaten records after seven games.