Bakgaga were looking to showcase their top flight prowess early on with a shot from a corner by Gift Motupa, but it failed to find the target.
They followed up with a shot cleared off the line after good work by Hassan Banda on the right-hand side.
Then, they had a perfectly legitimate goal incorrectly disallowed with TV replays clearly showing Motupa in the clear and level with the last defender.
Chances kept coming for them while they continued their inaccuracy with Lebogang Mabotja missing a free header.
Ayanda Dlamini was forced to his first save after 40 minutes which he pulled off outstandingly through a header from Abduragman White.
This scare led them to break the defence at the other end and set-up Rhulani Sidumo for an easy tap-in following a counterattack.
After sustaining the early pressure in the second half, Bakgaga threatened for a second when Mpho Kgoetyane saw his shot cleared off the line from a cross by Sidumo.
Motupa responded with another effort after being sent clear, but he fired directly at the goalkeeper moments later.
Sidumo came close to ensuring his brace, but was stopped by the crossbar after playing a one-two with Motupa after 73 minutes.
The Cape Town outfit also struck the upright after Dlamini was caught wanting, with Robyn Rode failing to finish off the error.
Substitute Tebogo Sodi made them pay with the second at the far post after being set-up by Motupa on 84 minutes.
The victory puts them in the head for the quarterfinals where they join NFD outfit Ubuntu Cape Town who knocked out AmaZulu on Friday.
Baroka: Dlamini, Kgoetyane, Banda, Sidumo (Makgaka 76', Sodi 81')), Mothupa, Mabotja, Madubanya, Moeti (Ngalande 54'), Kgaswane, Mdantsane, Motupa.
Subs: Vries, Sodi, Makgaga, Mapheto, Mosele, Ngalande, Mohwatseleng.
Steenberg: White, Van Reenen, Moegamat, Pietersen, Maqoko, Jodwana, Fredericks (Hendricks 76'), George, Basadien (Davids 83'), Qambela (Rhoda 46'), Heleni.
Subs: Ngcuka, Hendricks, Reid, Royston Rhoda, Robin Rhoda, Davids, Johannesen.