The Birds have not lost to Ea Lla Koto since 2009, and extended that record to seven League games with this valuable away victory, secured courtesy of a superb Katlego Mashego free-kick.
Stars dominated the opening exchanges and on 18 minutes only a terrific save from Greg Etafia denied them the opening goal, with the Nigerian tipping over a point-blank effort from Dove Wome.
A minute later Moeketsi Mvula had a free header in the box but put his effort over the top, while on 24 minutes the same striker tested Etafia with a low shot, but the Swallows goalie kept out the effort with another good save.
Just past the half-hour mark the dangerous Wome brilliantly controlled a long ball over the top of the defence and rounded Etafia before tumbling to the ground in hopes of winning a penalty. But the referee was not fooled by a blatant piece of diving from the Togo attacker, though he should have booked him for simulation.
The Birds were much more of an attacking threat in the second half and on 54 minutes Lerato Chabangu almost opened the scoring with an acrobatic volley, only for Kennedy Mweene to produce an excellent low save at his near post.
The home side remained potent on attack and should have broken the deadlock on 68 minutes when Wome put Mvula through on goal, but the young striker saw his angle quickly closed down by Etafia and pulled his shot wide of the target.
In the 75th minute the goal the game had been threatening finally arrived – and what a beauty it was. Mashego curled home a brilliant goal direct from a free-kick to put the visitors 1-0 up.
Stars created a few good chances to equalise, the best of which went Mvula’s way in injury time, but they were unable to convert them and have only themselves to blame for picking up no points from a match they mostly dominated.