The Scotland international’s goal in the final minutes of the encounter proved to be the difference between the two sides at Celtic Park.
The 25-year-old striker did not start the Scottish Premiership game and came on as a half-time substitute, as the Bhoys ended the match with 10 men.
RD: "When Leigh came on we were the more dangerous, he went behind them and in the end got the chance we needed to win the game."— Celtic Football Club (@celticfc) January 2, 2016
Over the course of the 90 minutes at Celtic Park, hosts Celtic had 57% of the possession, took 12 shots of which six were on target, and earned four corners.
Ronny Deila’s side are at the top of the Scottish Premiership table at the moment with 46 points from 20 matches. The Glasgow giants are three points clear of second-placed Aberdeen and also have a game in hand.
Celtic will take on Stranraer away from home in the fourth round of the Scottish Cup next weekend.