Goals from Bangaly Soumahoro and Ricardo Nascimento inside the opening seven minutes gave Sundowns a fast start, but they wasted a number of good opportunities before Geoffrey Sserunkuma grabbed what could be a vital away goal for the visitors.
Sundowns now go to Kampala next Saturday with the slenderest of leads, where a 1-0 defeat would see them ousted on the away goals rule.
Pitso Mosimane's side made the perfect start when Ivory Coast defender Soumahoro rose at the back post to head home a free-kick inside two minutes.
And it was 2-0 minutes later when Nascimento converted from the penalty-spot as Thapelo Morena was fouled in the box by Joseph Ochaya. Referee Janny Sikazwe had no hesitation in pointing to the spot and replays proved his decision to be correct.
A rampant Sundowns had the ball in the back of the net on 17 minutes when Leonardo Castro headed home Tebogo Langerman's cross, but Sikazwe ruled out the effort, accusing Percy Tau of interference in the build-up.
Sundowns had a few half-chances after that but found openings in short supply for the remainder of the first half and went into the break at 2-0 up.
Sundowns continued to apply pressure in the second period and after Hlompho Kekana flashed a shot wide, KCCA found their away goal as Sserunkuma side-footed home.
Sundowns should have restored their two-goal lead minutes later when excellent build-up play saw Tau with a clear sight of goal, but he put his shot wide.
Sundowns: Sandilands, Ngcongca, Nascimento, Soumahoro, Langerman, Mabunda (Laffor 84'), Kekana, Morena, Tau, T.Zwane (Zakri 71'), Castro (Modise 70').
Subs: Mweene, Nthethe, Mashaba, Vilakazi.
KCCA: Ochan, Okot, Kavuma, Awany, Ochaya, Kirabira (Nsibambi 65'), Ntege, Mutyaba, Majwega, Musamali, Sserunkuma (Okello 87').
Subs: Lukwago, Ssentongo, Kayizzi, Rukundo.