Swallows enjoyed a 2-0 lead at the break thanks to strikes from new signing Vladimir Mandic and Felix Obada.
However, Ea Lla Koto responded with interest via a brace from Adam Abdul-Basit and goal from Moeketsi Sekola at Goble Park.
After a slow start, Swallows went ahead in the 20th minute as new signing Mandic scored his first goal for the club with a scuffed shot that looped over goalkeeper Ayanda Mtshali.
Obada then doubled the advantage with a composed finish on the stroke of half-time.
Stars, though, pulled on back soon after the interval, as Sekola volleyed home from six yards out.
Adam then equalised with a superb volley from a tight angle in the 63rd minute before bagging the winner with a low strike 10 minutes later.