Nyandoro scored in the 85th minute for his first goal of the season, while Matthew Pattison's hard work in the centre of the park earned him the Man of the Match award.
Leopards were the best of the two sides in the first 45 minutes, as they looked to take the game to the Brazilians early on, and they had two long-range efforts in the first five minutes.
First, in the second minute of the match Khethokwakhe Masuku drove forward and tried his luck from about 35 yards out. Fortunately for Brian Baloyi in the Downs goal the shot just went wide as he scrambled across his goal-line.
Then two minutes later Samson Mofokeng watched his long-range shot just skim the wrong side of the upright.
Leopards’ passing was much more fluid than Sundowns’, but nonetheless the Tshwane side began to take control of the midfield, with Matthew Pattison doing the hard work in the middle of the park to give his side the ascendancy.
The Brazilians first real chance of the game came in the 29th minute, sparked by Pattison. After a good build-up Benedict Vilakazi found himself through on goal, 12 yards out and with only the keeper to beat.
The Leopards goalie Ayanda Mtshali, however, pulled off a fantastic save, diving to his right to palm the effort around the post.
Mtshali was called into action again seven minutes later with another great save, this time diving full stretch to his left to tip a 25-yard Pattison free-kick over the crossbar.
The best chance of the half fell the way of the Leopards two minutes into injury time. A free-kick was fired into the Sundowns box, and Baloyi fumbled the ball into the path of two Black Leopards attackers, who stumbled over each other, giving Baloyi the chance to make a fine double save.
Leopards dominated proceedings to a large extent in the second stanza, with Mofokeng proving to be the main danger man.
The Leopards striker should have put his side in front in the 56th minute when he showed some skill to beat a couple of players and put himself in a one-on-one situation with Baloyi.
But with acres of time and space he squandered the golden opportunity pushing his effort wide of the target from only ten yards out.
Mofokeng caused more trouble seven minutes later when he whipped in a dangerous low cross which Baloyi fumbled, but no other Leopard players were following up.
Then Sundowns stole the lead against the run of play, with their first clear-cut opportunity in the second half. Benedict Vilakazi head out a corner to Esrom Nyandoro on the edge of the box. The Zimbabwean took one touch to control the ball and placed a finely-chosen shot into the top right corner, 1-0.
After scoring Sundowns were able to hold onto their lead, stealing victory from Black Leopards on the day.