Swallows trailed 2-0 after 56 minutes on a chilly autumn night south west of Johannesburg before Augustine Mahlonoko halved the deficit with a tap-in.
Although Swallows lie third last in the 16-club table, they became the first side this season to score twice against the defending champions.
Teboho Mokoena put Sundowns ahead on 37 minutes with a drive from outside the area and Chilean Marcelo Allende doubled the lead after 51 minutes through a deflected shot.
The draw leaves Pretoria-based Sundowns needing 11 points from nine matches to win the Premiership for a seventh straight time and 14th season overall.
Sundowns now adjust their sight to Africa, leaving Johannesburg on Tuesday for Tunisia and a CAF Champions League semi-final first leg against Esperance this weekend.
© Agence France-Presse
Photo: Twitter @ProsportInt