Joel Masutha's charges paid the price for the miss, as Sandile Mthethwa broke the deadlock for the Chilli Boys in the 63rd minute with a volley at the near post after Callies failed to clear their lines inside the box.
Masutha responded with a triple change in the 68th minute, as he brought on Malwande Natemba in place of Nkoana, Njabulo Buthelezi came on for Pheko and Pogiso Mahlangu replaced Siyabonga Menziwa, to take the game to Chippa.
Mahlangu had a big chance to level matters for Callies in the 73rd minute with a free header inside the box that sailed over the bar after a cross by Keorapetse Sebone.
Chippa handed former Mamelodi Sundowns midfielder Oupa Manyisa his debut seven minutes before time in place of Phewa for fresh legs.
Bienvenu Eva Nga had a goal disallowed for Chippa in stoppage time for offside but they had done just enough to reach the final for the first time and will face the winner between Sundowns and Tshakhuma Tsha Madzivhandila.
