The once-powerful Birds dropped out of contention for top place in a promotion mini-league after losing 1-0 at Black Leopards.
A Roggert Nyundu goal after 32 minutes at a packed stadium in Thohoyandou condemned Swallows to lower-league football.
Swallows finished second last in the 2015 Premiership, forcing them into a double-round mini-league with Jomo Cosmos and Leopards, who came second and third in the second division.
Cosmos, owned and coached by 1980s South African football legend Jomo Sono, will gain promotion on goal difference if they win at Swallows on Wednesday.
Any other result would bring Leopards back to the top tier.
The South African Premiership offers unrivalled African domestic club football riches with multi-million-rand prizes up for grabs in the league and three cup competitions.
Original source: Birds’ wings clipped