Sundowns started brightly and took the game to the Zimbwean team, who were happy to sit deep. But far from parking the bus, Chicken Inn were dangerous on the counter-attack and caused problems, just as they did in the first leg.
Wayne Arendse gave the Brazilians the lead on the night in the 35th minute with a close-range header at the far post from Khama Billiat's deep free-kick to make the score 1-1 on aggregate.
Asavela Mbekile and Bangaly Soumahoro, the latter playing in a holding midfield role, were both booked after being drawn into necessary fouls as the visitors countered at pace.
Chicken Inn's goalscorer in the first leg Mitchell Katsvairo almost bagged a valuable away-goal just before half-time when he cracked the upright after another swift counter-attack.
Sundowns enjoyed more possession and created more chances in the first half but the game remained finely balanced with 45 minutes to go.
'CBD' shifted another gear in the second half as Leonardo Castro, Billiat and Keagan Dolly started knocking around the short passes and created openings, although nothing was really coming off as a few Castro passes went astray.
In the 56th minute Billiat played a one-two with Castro before seeing his shot crash against the upright, only to see Castro's follow-up shot fly over the crossbar under pressure from a defender.
Billiat kept at it and his persistence down the left created a chance for Anthony Laffor rushing in late at the far post, but the Liberian could not keep his first-time shot down.
Seven minutes from time Chicken Inn came close to snatching victory when Denis Onyango was called into action to produce a save, and fortunately the rebound fell behind another attacker and was put wide.
Billiat eventually made the difference right at the end.
After substitute Mashego pounced on a loose ball in a dangerous area, he sent Billiat through on goal. The Zimbabwean showed great close control and pace to get into the box where he was clipped by Passmore Bernard.
It was the 95th minute of the match as Mashego stepped up to the spot, and he made no mistake, burying it low and hard with his left foot to send Sundowns through to the next round.
Sundowns XI: Onyango, Mbekile (Mashego 90'), Nthethe, Arendse, Langerman, Soumahoro (S Zwane 46'), Kekana, Mashaba, Dolly, Billiat, Castro