The Urban Warriors, who were losing finalists in this competition in 2006, had to endure heavy pressure from the Buccaneers, especially in the second half.
Siphelele Mthembu pulled a goal back for Pirates with 14 minutes to go, but Ajax held on for the win to add to their 2000 Rothmans Cup and 2007 Absa Cup triumphs. For Pirates, it continues a run of eight years without a knockout trophy.
Khenyeza almost fashioned an incredible opening goal for Ajax in the first few seconds when he latched onto a ball over the top of the Pirates defence, but his cross was inches away from the on-rushing Sifiso Vilakazi.
Irvin Mhlambi failed to connect with a low cross at the other end in a bright opening to the game, while Sameegh Doutie flashed his shot from 25 yards wide.
But Ajax were ahead in the 10th minute when Khenyeza met Franklin Cale’s cross at the near post with an incredible finish as he fell backwards in turning the ball home.
And it was 2-0 on 16 minutes when Cale again crossed low, with the ball squirting through a clutch of players to Clayton Daniels at the back post. Daniels beat Pirates goalkeeper Moeneeb Josephs to the ball and squared a cross back along the goalline, for Khenyeza to force the ball home.
Sections of the Pirates crowd started calling for the substitution of Josephs, when really they should have been focusing on how their back four had let the stopper down on both goals, particularly the second when they had three chances to clear.
Pirates had four shots on goal in one single attack on 21 minutes, before goalkeeper Andre Petim finally turned the ball behind for a corner from Dikgang Mabalane’s angled effort.
It marked a good period of pressure for the Buccaneers, with Mabalane looking especially dangerous down the right wing. Benson Mhlongo’s header looped onto the top of the crossbar mid-way through the first half as Pirates seemingly edged closer to a goal.
Petim received a yellow card from referee Peter Mabuza for time wasting on 26 minutes, with his skipper Brett Evans following him into the book seconds later after contesting the decision.
Gilbert Mushangazhike smashed the ball against the top of the crossbar with a powerful drive after Nazeer Allie had put in a good block to stop a low drive from Teko Modise.
Khenyeza almost scored his hat-trick with a great turn to beat Lucas Thwala, but his low shot was past the post with Josephs off his line.
Vilakazi should have made it 3-0 four minutes before halftime when he rose to meet the corner, but headed into the side-netting, while at the other end, Petim made a brilliant stop from Modise, whose powerful volley was beaten away by the keeper.
Pirates coach Ruud Krol replaced Irvin Mhlambi with Bennett Chenene on 42 minutes as he looked to shake things up on the left.
Dipsy Selolwane forced a good save from Josephs a minute into the second half, while Mushangazhike flashed a 30-yarder over the bar at the other end.
Pirates hit the frame of the goal for a third time when Mabalane, easily their most impressive player on the night, shot low into the near post from a tight angle.
Mabalane crossed for Mushangazhike with 20 minutes remaining, but the striker could not get on top of the cross and the ball flicked off the top of his head.
Mothibantwa made a brilliant last-ditch tackle to deny Vilakazi, who looked to have been put through by Khenyeza, but seconds later Pirates were back in the game.
Substitute Mthembu took advantage of a wicked ricochet in the Ajax box to coolly side-foot home with 16 minutes remaining and set up a fantastic finish.
The youngster had the ball in the back of the net minutes later, but the goal was correctly ruled out for offside.
By now Pirates were laying siege to the Ajax goal and with the Urban Warriors players cramping all over the park, Martin Carelse made a last-ditch block as Mushangazhike latched onto a cross at the near post.
Carelse set Khenyeza free on 86 minutes, but Josephs rushed off his line to thwart the danger. The Ajax striker claimed he was fouled and replays suggested contact was made.
If the match officials had seen the incident clearly, there would surely have been a red card for the goalkeeper, but a goal-kick was given as the ball trickled wide.
Chenene should have forced the game into extra time with just seconds remaining, but he put his shot wide when a cross into the centre would have seen an easy tap-in for Mthembu.