Celtic opened the scoring thanks to Liel Abada. The Israeli winger got on the end of a lovely cross from Jota on the left hand side to give Celtic the lead.
Just moments before, James McCarthy suffered a sore one after a bad tackle. However, the Celts pressed on and took a deserved lead thanks to Abada.
The 19-year-old has been a revelation since signing this summer.
United struck back shortly afterwards as Ralston was beaten on the right, only for Harkes to header the ball beyond Hart.
Celtic went up the other end in the hunt for another goal with Abada’s cut back to Ajeti from six yards out looking certain for a goal; however, the Swiss striker blazed over.