The goal was scored by Esrom Nyandoro.
The match was exciting with both sides defending well but there were few shots at goal throughout. A draw would probably have been a fair result.
The goal was scored by a Nyandoro penalty kick in the 48th minute after the referee correctly adjudged that Didier Mbendje had handled the ball in the area.
Celtic nearly pulled a goal back in the 61st minute when a Lebohang Kukame bicycle-kick was brilliantly saved by keeper Brian Baloyi.
The result has Sundowns mid-table on 8 points while Celtic remain near the top on 13 points.