Khama Billiat opened the scoring but Bernard Parker equalised before half-time, before Bangaly Soumahoro handed Chiefs the win with a bizarre own-goal.
Chiefs showed early intent as they took up a high tempo in attack, using their wingers to good effect as they won a few fouls in good areas.
Sundowns, however, had the first real chance as Soumahoro picked out Tiyani Mabunda in the box, with the latter misdirecting his header over the cross bar.
Shortly afterwards, Erick Mathoho had a similar chance at the opposite end as Siphiwe Tshabalala whipped in a free-kick but the defender's header was off target.
Billiat then marked his return with a goal in the 26th minute as his shot from outside the box took a hefty deflection off Lorenzo Gordinho's trailing leg to leave Itumeleng Khune wrong-footed.
The lead didn't last long as Parker excellently turned home Edmore Chirambadare's low cross to level matters less than 10 minutes later, leaving Kennedy Mweene with little chance at his near-post.
Joseph Molangoane then beat his marker to find an advancing George Maluleka on the edge of the area, but the resultant header was too tame to really test Mweene.
Three minutes before the break, Mweene was forced to tip Parker's rifled left-footed effort angled towards the near-post out for a corner, before Downs cleared their lines with the scoreline at 1-1.
Exchanges on both ends of the pitch saw Khune and Mweene both called into action to keep the scoreline unchanged early in the second half.
Themba Zwane had a great chance to get on the scoresheet after being played into space by Percy Tau, but the winger made a complete mess of his shot as he sent the ball high and wide from close range.
Khune made a great block to deny Zwane just after the hour-mark, as he rushed of his line to close the angle after the Downs attacker rounded Mathoho with an excellent turn into the box.
The visitors were then forced into a costly error as substitute Gustavo Paez applied good pressure on Soumahoro, who then played the ball into his own net with Mweene not expecting the back-pass.
The Brazilians turned up the pressure as Khune produced a fine save to deny Hlompho Kekana's goal-bound free-kick in stoppage time, and then foiled the skipper from range after the shot took a slight deflection off Tau.