Lebohang Kukame scored for the hosts, with Bernard Parker netting for Thanda.
Celtic started the better of the two sides and went ahead in the seventh minute when Kukame scored from close range following a superb low cross by Tumelo Nhlapo.
However, Phunya Sele Sele’s joy was short-lived as the visitors drew level three minutes later when Katlego Loke beat the offside trap before setting up Parker to slot the ball into an empty net.
Gary Goldstone almost restored Celtic’s lead in the 23rd minute, but the defender’s header was well saved by Aime Kitenge.
Kitenge was then stretchered off the field in the 32nd minute following a collision with Celtic’s Lebo Ramolesa and he was replaced by Mandlenkosi Tsengwa.
Parker wasted a good chance to put the visitors ahead a minute before the break when he shot over the bar.
The score remained 1-1 at the break.
Both sides struggled to hold onto possession in the opening stages of the second half, with Moses Spandeel the first to threaten in the 60th minute when he headed Tumelo Tumelo Nhlapo’s cross straight at Tsengwa.
Tsengwa was the busiest of the two goalkeepers as Celtic finished the game strong, with the visiting keeper making saves from Patrick Malokase and Kamohelo Mabuya.
However, it was Parker who wasted the best chance of the second half in the final minute of the game when he headed wide from inside the six yard area.
Celtic move to 18 points, six off the pace set by leaders Ajax Cape Town, while Thanda remain bottom on 10 points but are now just a point away from 15th placed Platinum Stars, who were given a 6-2 thrashing by Swallows.