The hosts opened the scoing through Geoffrey Sserenkuuma before Anthony Laffor struck late on to level the match at 1-1 but hand Downs a 3-2 win on aggregate.
Kampala had the first effort on goal through Joseph Ochaya, whose shot went narrowly wide of the mark in the sixth minute.
The visitors were forced into an early substitution as Wayne Arendse took a knock and was replaced by Bangaly Soumahoro in the 10th minute.
In the 12th minute, Themba Zwane forced a fine point-blank save from Ochan as Downs looked to gain the early advantage.
Five minutes later Hlompho Kekana came close to finding an opener with a trademark pile driver from range, but Benjamin Ochan was up to the task as he palmed the effort to safety.
Soumahoro had the ball in the back of the net in the 26th minute but the goal was ruled out after the defender was adjudged offside.
The hosts opened the scoring on the half-hour mark through Geoffrey Sserenkuuma tapping home from Brian Majwega's cross.
Kampala held on to go into the half-time break 1-0 up as they looked to shut the back door.
The Brazilians went in desperate search of an equaliser as they risked being eliminated on away goals rule, but the Kasasiro Boys' defence held firm.
Substitute Anthony Laffor finally found the back of the net with 10 minutes left on the clock, to ease the threat of an early exit for the defending champions.
The draw means Pitso Mosimane's men have now advanced to the Champions League group stages for a second year running.
KCCA: Ochan, Okot, Kavuma, Awany, Ochaya, Mutyaba, Kirabira, Mucureezi, Okello, Majwega, Serukuuma.
Sundowns: Sandilands, Ngcongca (Laffor 46'), Nascimento, Arendse (Soumahoro 10'), Langerman, Kekana, Mabunda (Mashaba 68'), Morena, Zwane, Zakri, Tau.
Subs not used: Mweene, Nthethe, Modise, Castro