It is Stars' first loss of the season at Charles Mopeli Stadium in Phuthaditjhaba, where they are difficult to beat.
The Birds move up to fourth on the log, on 33 points, beneath Kaizer Chiefs and Orlando Pirates on goal-difference.
The on-form Mathebula got on the end of a cross from Siyabonga Nomvete to hit home after 14 minutes of play.
Ea Lla Koto went in search of the equaliser, and Mpho Makola came closest, but was denied by Swallows goalkeeper Greg Etafia.
Etafia was called into action again just before half-time, when Boitumelo Sekgobela had a go at goal, but the Nigerian was up to the task.
Bennett Chenene went narrowly wide for Swallows, before Mathebula's free-kick was saved by Bruce Mtshali in the Stars goal.
Around the hour-mark Tshidiso Mosikidi and Danny Mbo both squandered chances to equalise for the hosts, but both shot wide, before Mosikidi tried a long-range effort that went just wide of goal.
Stars were desperate to salvage a point, and Nomvete took advantage, creating something out of nothing against the run of play, but his final shot was saved well by Mtshali.
Stars remain in seventh place on the table, with 29 points.