Bakgaga made wholesale changes, with only goalkeeper Oscarine Masuluke, Bonginkosi Makume and Ananias Gebhardt remaining from the side that drew with Cape Town City last time out.
Ashley Cupido came close to grabbing an early lead for Spurs in the seventh minute after receiving a cross from Cohen Stander but his first-time side-footed shot at the near post was crucially blocked.
Gerald Phiri Junior almost broke the deadlock for Baroka on the half-hour mark with a threatening free-kick that took an awkward bounce close to the goal but shot-stopper Lincoln Vyver managed to parry it away.
Thendo Mukumela was unlucky not to give Ian Taylor's troops the lead two minutes before the break with a powerful header in that was acrobatically parried over the bar by Masuluke.
The opening goal did arrive before halftime as Richard Mbulu broke the deadlock for Matsimela Thoka's with a powerful volley after getting on the end of Phiri Junior's flick-on.
The game opened up early in the second stanza, with both sides missing big chances but Cupido finally levelled matters for the visitors just before the hour-mark with a first-time strike across goal at the back post after a cross by Stander.
Chumani Butsaka came close twice to giving the Cape Town side the lead in the 67th minute after going on a solo-run inside the box and unleashed a low strike that was saved by Masuluke whilehe had another chance from the rebound at close range but struck it wide at the back post.
Mukumela had a chance to snatch the winner for Spurs in the last eight minutes with a powerful strike inside the box that was saved by Masuluke at full stretch, which sent the match into extra-time..
Mukumela had a glorious chance to give the visitors the lead in the 14th minute of extra-time after going clear on goal from a counter-attack but his low shot was saved by Masuluke.
After Evidence Makgopa squandered a big chance hosts in the last action with a close-range header, he match went to a penalty shoot-out where Vyver was the hero for Spurs, as he saved two penalties which allowed Riyaaz Koopstadt to slot home the winning spot-kick.
Baroka: Masuluke, Kgoetyane, Seema, Makume, Gebhardt, Patjie, Phiri, Monama, Afonso, Ntemane, Mbulu.
Subs: Chipezeze, Mogale, Bowali, Mgaga, Mahlonoko, Farmer, Kamatuka, Masiya.
Spurs: Vyver; Stander, Da Silva, August, Fisher, Mukumela, Khumalo, Mfecane, Butsaka, Mosiatlhaga, Cupido.
Subs: Johnson, De Oliveira, Velebayi, Norodien, Mncwango, Sali, Johannes, Koopstadt, Madikane.