Leigh Griffiths gave Celtic the lead with just 12 minutes on the clock. The 30-year-old took the ball from Moi Elyounoussi and fired it beyond Fulton in the Hamilton Accies net.
Griffiths will be hoping to prove the Celtic support that he still has a future at the club as a squad overhaul looms. Fans are still awaiting the outcome of the management review in January so Neil Lennon will be hoping a convincing scoreline will help his cause.