The two sides were deadlocked at 3-3 after regulation sides, with Ajax striking via Thembinkosi Fanteni and a brace from Khama Billiat, while Usuthu fought back through Thamsanqa Teyise and a brace from Goodman Dlamini.
Roger Palmgren’s men then managed to hold their nerves during the penalty shootout while Keamogetse Wolff and George Akpabio failed to convert for the Urban Warriors.
Kapini made two great saves early in the first half, parrying away a great free-kick from Billiat in the 7th minute and another shot from Fanteni in the 14th minute.
Usuthu also created their chances with Andile Khumalo’s shot being cleared off the line by a defender in the 15th minute, while Thamsanqa Sangweni forced a save from Sean Roberts with a well-struck free-kick four minutes later.
The home side continued to dominate possession in the middle of the park, but it was the visitors who broke the deadlock in the 43rd minute Fanteni shrugged off his marker before drilling a low shot past Kapini.
AmaZulu had a chance to level matters on the stroke of half-time via a swerving free-kick from Bongani Mbele, but his effort went just wide of the target.
Both sides then squandered their early chances in the second half before the Urban Warriors extended their advantage in the 62nd minute when Fanteni played Billiat through, and the Zimbabwean didn’t disappoint as he calmly placed the ball beyond Kapini’s reach.
Despite being two goals down, Usuthu continued to play positively and managed to reduce the deficit eight minutes later when Teyise headed home from a Goodman Dlamini corner.
The home side levelled matters in the 79th minute when the self-same Dlamini latched onto a great pass from Kagiso Senamela before firing a low shot on target. Roberts managed to get a hand to it but there was nothing he could do as Dlamini fired home from the rebound.
However, Ajax took advantage of their opponents’ excitement and quickly restored their lead two minutes later when Billiat broke the offside trap before getting the slightest of touches to get the ball past Kapini.
But there were still more twists to the tale as AmaZulu found an equalizer in added time when Goodman Dlamini fired a powerful shot from the edge of the box to grab his second goal of the match.
Both sides were unable to add to their tally in extra-time and in the end the tie had to be decided on penalties where Kapini came through for his side once again as he saved the fourth penalty from Wolff.
Akpabio had to convert the fifth penalty to keep Ajax in the game but instead sent his effort wide to send Usuthu to the last 16.
AmaZulu (0) 3 (Teyise 70’, G Dlamini 79’ 91’) Ajax Cape Town (1) 3 (Fanteni 43’, Billiat 62’ 81’)
AmaZulu: Kapini, Mokoro, Mbele, Nyadombo, Teyise, Sangweni, Khumalo (Lewis 70’), Shipahu, Zwane (Senamela 56’), G Dlamini, Vilane (A Dlamini 65’)
Ajax: Roberts, Hlatshwayo, Booth (Wolff 46’), Allie, Jenniker, Mokeke, Rusike, Vilakazi (Scott 61’), Fanteni (Akpabio 71’), Alexander, Billiat