It was a fiesty encounter at the Pittodrie Stadium as both sides had a player sent off, but it would be Brendan Rodgers and his Celtic team who would walk away victorious on Sunday.
Dembele opened the scoring for the Scottish giants in the 37th minute, heading home a cross from James Forrest at the back post.
Celtic and Aberdeen would then exchange chances until the leaders were reduced to 10-men with 15 minutes left after Mikael Lustig picked up his second yellow card.
However, the visitors would cement their lead in the 83rd minute when Tierney fired his shot into the back of the net.
Aberdeen were obviously frustated and tensions would boil over soon after the goal when their debutant substitute Sam Cosgrove was sent off for a lunge on Scott Brown.
The win restores Celtic nine-point lead over second-placed Rangers, who play one another in a fortnight, while Aberdeen remain in third with 52 points.