Downs enjoyed plenty of possession early on and were unlucky not to go ahead after a double save from Khanya Mini denied George Lebese.
That was before Jeremy Brockie saw his frustrations in front of goal for his new club continuing following a misplaced header.
A poor clearance by Siyabonga Zulu landed straight to Joseph Chikile, who ran at the defence and beat Kennedy Mweene with a fortunate bounce of the ball to tap home into an empty net.
Great combination by Themba Zwane and Lebese played in the latter but Mini came up with another close-range save.
Stand-in Sundowns coach Manqoba Mngqithi made his first tactical change, taking out Anele Ngcongca for Thapelo Morena on 30 minutes.
Bees did the same bringing on Sonwabo Maqokolo for Sonwabo Vandala minutes before half-time, which presumably was for tactical reasons.
The action kept piling up at their end with Mini called to action for the second time to prevent Anthony Laffor from finding the equaliser from close proximity.
The young shot-stopper then denied Lebese once again after he stretched his right leg to divert the incoming shot to touch a minute from the break.
It took Downs less than 60 seconds after the restart to level the scores with a stunning strike from captain Hlompho Kekana after good close control.
The Eastern Cape side were looking to reclaim the lead as they fired in shots from all angles shortly before the hour mark.
Mngqithi made his second change from the bench, the highly-rated Gaston Sirino filing in for Lebese after 60 minutes.
With time running out, the home side were looking for control on the scoreboard and Kekana lined-up for another shot from range but Mini was well-prepared to avert the effort from goal.
Bees broke on a counterattack and played in Mutli Mtule, who came within a whisker from finding the net, but his curling effort sliced wide.
The dominance from Downs was reinstated when Morena gave them the lead for the first time after starting and finishing off his move following a cut-back from Brockie on 76 minutes.
Bees looked for a way back and after pressing forward for the equaliser, Downs stood their ground to march into the last eight.
Bees: Mini, Zondeka, Bisha, Mhlakaza, Gwale, B. Dlamini, Tshange (Dlamini 49'), Mothabasi, Mtutle, Vandala, Chikile.
Subs: Kanana, Maqokolo, S. Dlamini, Moeti, Ncomani, Ntingiso.