The win moves Celtic three points clear of arch-rivals Rangers ahead of Sunday morning's (AEDT) Old Firm derby clash and all but ensures they will end 2018 on top of the Scottish Premiership.
However, it could've been very different at Pittodrie for the Hoops.
Sinclair helped Celtic off to a perfect start when he hit the back of the net after only six minutes, but Aberdeen were soon back level thanks to a Stevie May penalty.
Tom Rogic, who played the full match in his final game for the club before joining the Socceroos squad in the UAE, struggled to make an impact in his usual attacking midfield position.
The match was balanced on a knife edge until the final 14 minutes of the match exploded into a flurry of goals.
Celtic reclaimed the lead on 76 minutes when Sinclair tapped in a James Forrest cross, yet once again Aberdeen fired back from the penalty spot.
Odsonne Edouard made it 3-2 for Celtic in the 87th minute and Sinclair claimed his hat-trick in the 88th minute to seemingly wrap up all three points for the Brendan Rodgers coached side.
Aberdeen gave the visitors a final scare when Lewis Ferguson scored in the 90th minute, before James Wilson missed the chance to snatch an incredible draw when he fired over the cross bar with the last kick of the game.
However, it wasn't to be for the home side as Celtic clung on for the win and top spot on the ladder.
