The nimble-footed William Twala, who was a constant thorn in the flesh of the Stars defence, scored the match’s solitary goal.
Chippa piled pressure on Stars from the opening whistle and came close to taking the lead through Mvelase who unleashed a pile driver from a distance but narrowly missed the target.
Moeketsi Sekola replied for Stars in the fifth minute but his shot from afar was deflected out for a corner which Ea Lla Koto put to waste.
Stars had another great chance in the ninth minute, Richard Henyekane had a great exchange of passes with Sekola, who played a through-ball for the bulky striker.
Henyekane, however, lost his footing inside the box and the keeper Mbongeni Mzimela cleaned out the danger.
Chippa were forced to make a change in the 20th minute when their talisman David Zulu failed to shake off a knee injury suffered earlier in the match and was replaced by Lucky Khune.
Sekola was at it again in the 26th minute but his final touch was a disappointing one as his shot lacked power and Chippa goalkeeper Mzimela made a comfortable save.
In the 32nd minute goalkeeper Mzimela fumbled a cross and the ball fell kindly for the Stars player, Thabo Moloi, who blazed his effort wide off an open goal.
William Twala beat the Stars offside trap and made a great run before he fired a low effort that was impressively tipped out for a corner by goalkeeper Ayanda Mtshali in 37th minute.
In the second half, Chippa picked up where they left off and were rewarded in the 47th minute when Twala beat Mtshali to give Chippa the lead in the 47th minute.
Stars had a chance to level matters in the 59th minute when an intelligent looping ball from Henyekane found Moeketsi inside the box but the midfielder failed to connect and Mzimela collected with ease.
Moeketsi came close again in the 72nd minute as he beat his marker and took a strong shot at goal, Mzimela blocked out for a corner.
Stars had to play the remainder of the match with 10 men after Robert Sankara was sent off after receiving a second yellow for a foul on Twala in the 75th minute.
Despite being a man down, Stars terrorised Chippa in the dying minutes but the Chilli Boys’ defence was resolute to hold on to their lead until the end.
The win takes Chippa to fourth on the table with 20 points from 12 matches, while Stars remain in the relegation zone with just 11 points.
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