The Scottish champions took the lead three times in a thrilling clash but City hit back each time to snatch a 3-3 draw.
Celtic were ahead in the third minute when Scott Sinclair's free-kick was volleyed across goal by the unmarked James Forrest and Erik Sviatchenko's header deflected in off Dembele's chest.
It was the first time that City had fallen behind all season but they were level nine minutes later when Aleksander Kolarov's scuffed shot trickled into the path of Fernandinho and the Brazilian tucked the ball past Craig Gordon.
But the home side were back in front in the 20th minute when Kieran Tierney's shot deflected off a sliding Sterling and past Claudio Bravo at his near post.
The England international made amends eight minutes later when he raced onto David Silva's through ball before his quick turn deceived the challenges of Tierney and Gordon and he tapped into an empty net.
A minute after the restart Celtic were ahead again when Kolarov failed to deal with Tierney's cross and Dembele hooked the ball into the net.
City hit back again 10 minutes later when Nolito tapped into the net after a Sergio Aguero shot was saved by Gordon.
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