Thabiso Nkoana struck a brace before Abbubaker Mobara added a third after the break for the Urban Warriors, who were recently handed their first Absa Premiership loss of the season by Aces.
Ajax took control early on this time around, as Nkoana netted with a brilliant right-footed finish in the sixth minute following some poor Aces defending.
Nkoana doubled their advantage in the 18th minute as he headed past Energy Murambadoro, with Tashreeq Morris again providing the assist.
The hosts continued to dominate, and killed off the match in the 75th minute as young defender Mobara combined nicely with his teammates before unleashing a powerful shot past Murambadoro.
Roger De Sa's men joined Orlando Pirates, Kaizer Chiefs, AmaZulu, Mamelodi Sundowns, holders Platinum Stars, SuperSport United and Bidvest Wits in the quarter-finals of the competition, with the PSL to decide the next match-ups via a draw on Monday.