Leopards showed up with a few changes in Lifa Hlongwane, Lehlogonolo Maselesa and debutant Mohammed Anas, while Given Thibedi returned to the Swallows midfield.
Dylan Kerr's side signalled their intentions clear six minutes in when Onyedikachi Ononogbu took a through pass from Masalesa in his stride to volley into the roof of the net.
Then, an early blow forced Kerr to reshuffle his stall after Sibusiso Khumalo was stretchered off from a knock minutes later and saw Pentjie Zulu replace the versatile player.
Leopards nearly surrendered the lead before the midway stage when a low ball from the left rolled to an unmarked Zaphaniah Mbokoma, but King Ndlovu pulled off a miraculous save.
The Dube Birds had the home side under their spell on the half-hour mark after a low shot in the area from Vuyo Mere forced Ndlovu into an outstretched save.
Ruzaigh Gamildien continued his scoring run three minutes to the break after he sent a low cross from Thabo Matlaba into the roof of the net.
Swallows' dominant first-half display carried over to the second stanza after Kgaogelo Sekgota's blistering shot from the near side of the box cracked the woodwork.
The Dube Birds opted for fresh attackers midway in the second half, as Thabo Mosadi and Joseph Mhlongo came on for Mbokoma and Sekgota respectively.
This intervention from Brandon Trutter paid off 20 minutes from time after Mhlongo dropped a shoulder on the near side to curl into the far corner of Ndlovu's net.
Leopards battled to get an equaliser as time started to run out, but the Dube Birds held their nerve to bag all the points.
Leopards: K. Ndlovu, Makobela, Khumalo, Gyimah, Douhadji, Masalesa, Maluleke, Karuru, Anas, Ononogbu, Hlongwane.
Subs: Muleka, Zulu, Abubakar, Mthethwa, Thutlwa, T. Ndlovu, Makgetlwa, Kabwe, Nthatheni.
Swallows: Vries, Mere, Matlaba, Letlabika, Ngcobo, Mokoena Sekgota, Mthethwa, Thibedi, Gamildien, Mbokoma.
Subs: Wynne, Mosadi, Seabi, Hlanti, Mahlatsi, Gozar, Nyatama, Mhlongo, Sait.