It was a deserved win for Stars, whose victory came thanks to goals from Robert Ng'ambi, Siphelele Mthembu and Benson Mhlongo. Lerato Chabangu scored a consolation for the visitors.
The home side netted first on five minutes as Joseph Malongoane's corner was expertly headed home by Ng'ambi, the Malawian international rising above Giorgi Nergadze to score.
Swallows almost scored when neat interplay between Lefa Tsutsulupa and Bennett Chenene saw the latter break the Stars defensive line, but his scuffed shot came off the foot of the post.
It was 2-0 for Stars just before the half-hour mark when Ng'ambi broke down the left-flank and his cross was perfect for Mthembu to side-foot home.
Nomvete should have pulled one back for Swallows when Stars goalkeeper Siyabonga Mpontshane dropped a routine long-ball at the feet of the Bafana Bafana striker. But with the goal gaping, he could only direct his shot onto Dikwena centre-back Thabiso Semenya, who had taken up a position on the line.
Stars then made the points safe when Mhlongo scored in his first outing for the side. Ngwepe swung over the corner and Mhlongo beat Ashraf Hendricks in the air to head past Etafia and into the far corner of the net.
Chabangu did pull a goal back as his fired home a wonderful free-kick from 25 yards, finding the top corner with a superb dink over the wall that left Mpontshane leaden-footed. Vuyo Mere was adjudged to have handled the ball on the edge of the area.