Elias Pelembe scored the only goal of the match deep into the second half in a match that Celtic had to finish with ten men following the dismissal of midfielder Alfred Ndengane.
The Brazilians profited from an unfortunate situation from the home team at the back as Elias Pelembe gave Sundowns the lead with 70 minutes gone.
Five minutes later Modise thought he had scored after doing everything right and showing composure but Tinyeb did well to safeguard his goal.
Celtic held on to the 1-0 loss and escaped conceding more goals.
Moroka Swallows lost 2-0 to Chippa United