Burkina Faso defender Robert Sankara scored the only goal of the game in the second half.
For Tuks, a second defeat at home and yet to pick up their first points on home turf, coach Steve barker will be disappointed when the hosts had dominated for large parts of the game.
There was little to shout about in the opening stages and the fans were made to wait for the 29th minute for Tuks to test Stars through Geofrey Massa, who was denied a stunning free-kick by the outstretched palm of goalkeeper Ayanda Mtshali.
Stars replied with a long-range effort of their own as Moeketsi Sekola powered a free-kick from more than 30 yards out, and it took a diving save from Washington Arubi to keep out the rocketed effort.
That was it to be all for the first half as the pair went into the break goalless and struggling to make any real impact.
Stars looked better after the break but still failed to inspire in front of goal.
Tuks were eventually undone by a corner in the 76th minute as a defensive lapse cost them the goal; Sankara heading home strongly from dead in front to steal the points for the visitors.