A brace of goals from Yassine Khenissi sealed the victory for the visitors, while Sibuiso Vilakazi was on target for Sundowns.
Esperance now head the pool with seven points, followed by Sundowns with four. Ethiopia's St George (two points) and AS Vita Club (zero) are in action in Addis Ababa on Sunday.
It took just six minutes for the visitors to get in front. Thabo Nthethe was off the pitch receiving treatment and Khenissi took advantage as he rifled the ball home.
Sundowns started to dominate the possession and found an equaliser on 21 minutes when some excellent passing saw Percy Tau feed Vilakazi and the Bafana Bafana star side-footed into an empty net.
Leonardo Castro had an excellent opportunity to give Sundowns the lead when he was played into space, but slipped at the vital moment to cap a disappointing night for the Colombian, who looked well off the pace.
Esperance then earned a penalty with a minute remaining when Bangaly Soumahoro committed a foul and Khenissi easily beat home goalkeeper Denis Onyango from the spot.
Sundowns are next in action away at Esperance on June 21.
Sundowns: Onyango, Ngcongca, Madisha (Soumahoro 45'), Nthethe, Langerman, Morena, Vilakazi, Mabunda, T. Zwane, Tau, Castro.
Subs: Mweene, Hachi, Mbekile, Mohomi, S. Zwane.