The Birds made only one change to the side that drew with Maritzburg United, as Musa Nyatama replaced the suspended George Matlou while Bakgaga also made one alteration, as Dan Ndlovu had a rare start.
Baroka extended their winless run to eight matches, with Kgoloko Thobejane getting his first point back in charge with a draw against Orlando Pirates while the Birds' new era started with a point against Maritzburg United.
Swallows were threatening in the opening exchanges and Mwape Musonda had a chance to give them the lead in the 16th minute with a header that was saved by goalkeeper Oscarine Masuluke.
The visitors kept on asking questions in the closing phase of the first stanza but they could not get clear opportunities, as the sides went to the halftime break goalless.
Swallows changed their setup in the 64th minute with a double change, as Given Thibedi replaced Austin Muwowo in a tactical tweak while Keletso Makgalwa came on for Lebohang Mokoena for fresh legs upfront.
Makgalwa eventually broke the deadlock for the Birds five minutes later with a strike in the box after he was setup by his fellow Sundowns loanee Grant Margeman.
Swallows managed to hold on to their slender lead in the closing stages, as they moved up to 14th on the log, three points ahead of bottom side Baroka.
Baroka: Masuluke, Makume, Sithole, Mgaga, Dlala, Shozi, Masiya, Makgopa, Ndhlovu, Bobete, Farmer.
Subs: Chipezeze, Seema, Sibiya, Goldstone, Kambala, Chauke, Nikitaridis, Ngubane, Monama.
Swallows: February, Nyatama, Margeman, Langerman, Matlaba, Musonda, Mokoena, Sasman, Muwowo, Letlabika, Mahlatsi.
Subs: Ngobeni, Thibedi, Saleng, Mohamme, Gamildien, Sibiya, Makgalwa, Mosadi, Ndlovu.