Nigerian striker Kelechi Iheanacho scored the winning goal as Celtics go level on points with Heart of Midlothian at the top of the Scottish Premiership.
Jamie McGrath was the latest Hibs sinner with a lunging challenge on Alastair Johnston after just 21 minutes.
The reigning champions looked set for an easy victory when Daizen Maeda scored his fourth goal in three games soon after.
But Joe Newell netted a controversial equaliser – where he seemed to control the ball with his hand – just before the break, only for Kelechi Iheanacho to secure the close-range winner.
It means Celtic only now trail Hearts on goal difference before the long-time leaders host Rangers, who are four points behind in third, on Monday.
Hibs, meanwhile, are left six points adrift of fourth-placed Motherwell and only two clear of Falkirk in the race for European qualification.
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