Swallows climbed out of the DStv Premiership drop zone after they battled back from two goals down to beat Baroka 3-2 at the Dobsonville Stadium in Soweto on Sunday.
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Bakgaga looked to have the upper hand in this relegation six-pointer when Sekela Sithole opened the scoring in the 20th minute before Richard Mbulu doubled their advantage early in the second half.
However, Dylan Kerr's side were back on level terms just after the hour mark thanks to a quick-fire brace from Mwape Musonda and Musa Nyatama completed the stunning comeback win three minutes from time.
The Dube Birds traded places with TS Galaxy to move up to 14th in the standings on 23 points, five clear of the Limpopo outfit, who were dealt a gut-wrenching blow to their survival hopes.
Swallows came into the encounter on the back of two successive draws and they nearly hit the front on 10 minutes when Musonda struck the upright after making contact with Grant Margeman's cross.
But it was Baroka who broke the deadlock 10 minutes later with the first real chance as Sithole slotted past Jody February from inside the box.
The hosts looked to respond and Matlala Makgalwa forced Elvis Chipezeze into a fine save with a snapshot from outside the area on 31 minutes, with Bakgaga throwing all 10 outfield players behind the ball for the remainder of the first half to protect their lead.
One goal became two shortly after the restart when Mbulu beat February from inside the box after being picked out by Evedince Makgopa in the 49th minute.
The Soweto club quickly got their act together and pulled one back through Musonda in the 62nd minute after being set up by Nyatama, who combined with the striker again moments later to restore parity.
Nyatama was playing a blinder as he hit the frame of the goal from long range on 74 minutes before eventually finding the back of the net at the death with an effort from inside the box to clinch a dramatic victory.
Swallows (3) 3 (Musonda 62', 63', Nyatama 87')
Baroka (1) 2 (Sithole 20', Mbulu 49')
Swallows:J. February, D. Solomons, W. Letlabika, J. Sait, Y. Sasman (F. Basadien 77'), K. Mahlatsi, G. Khupe (M. Nyatama 50'), G. Margeman (K. Ndlovu 50'), M. Makgalwa (L. Mokoena 50'), M. Musonda (S. Wambi 90'), M. Saleng.
Baroka:E. Chipezeze, B. Mphahlele, B. Makume, D. Farmer (V. Sibiya 82'), S. Ngubane, M. Kambala, B. Bobete, T. Masiya (R. Mbulu 38'), E. Makgopa, S. Sithole (S. Maluleke 82'), D. Ndlovu (N. Mgaga 71').