The victory moves Usuthu out of the relegation zone for the first time this season and comes following their loss in the Nedbank Cup against third-tier side Tembu Royals in midweek.
By contrast, Swallows were coming off a 3-2 victory over Orlando Pirates, but never quite got into top gear in this game.
Makhosonke Bhengu and Malongoane netted for Usuthu, while Bennett Chenene scored for Swallows.
There were few chances in the opening period, but AmaZulu went into the break ahead. Malongoane fed Bhengu in the area and the forward netted from an acute angle, AmaZulu’s 10th goal of the season.
Swallows found an equaliser with 18 minutes on the click when Obada fed Bennett Chenene and the winger applied an excellent finish on the run.
But the visitors would not be denied and they were back in front with eight minutes remaining on the clock.
Ayanda Dlamini saw his shot blocked by Greg Etafia in the home goal, but Malongoane was on hand to score from the rebound.