Abafana Bes’thende surged into a two-goal lead through a 13th-minute penalty from Thanduyise Khuboni – this after Bongi Ntuli was fouled in the area.
The striker then got his name on the scoresheet seven minutes later after beating the offside trap and firing past Greg Etafia.
The Birds pulled a goal back late on when Luvhengo Mungomeni headed home Lerato Chabangu’s free-kick in the 78th minute, but they were unable to complete a come-back despite some late pressure.
The result sees Swallows drop to third place on the log on 15 points, two behind leaders Mamelodi Sundowns.
Arrows lift themselves off the bottom of the standings, though only to second-last on seven points. Champions League finalists Orlando Pirates are now bottom, having played just three matches.
Swallows are only in league action again on November 22 when they take on Ajax Cape Town away, while Arrows face SuperSport United away from home this coming Saturday.