Odsonne Edouard made it 2-0 to Celtic after getting the break of the ball in the Hamilton box. Leigh Griffiths slid his strike partner in but the sliding Conroy didn’t manage to put the Frenchman off, who cut back and fired the ball beyond Fulton.
It was a tidy finish but Celtic will hope they can build on from here and get a few goals.
Edouard has been linked with a move away from the club as the January transfer window nears an end.
Elsewhere, Rangers are ahead in Leith through Alfredo Morelos – who had a red card offence go unpunished in the first half.
