The NFD leaders, who beat Chippa United in their tournament opener, claimed another Absa Premiership scalp via goals either side of the break from Jacky Motshegwa and Man of the Match Loyiso Simandla.
Arrows ended the match with ten men as Thabo Molefe was shown a straight red card for a stray elbow on Motshegwa with seven minutes left.
Abafana Bes'thende showed early intent, as Nduduzo Sibiya struck the upright in the sixth minute after a strong run down the left flank.
At the other end, Mfundhisi Chauke tested Ricardo Goss with a useful free-kick in the 15th minute.
The visitors then stole ahead on the stroke of half-time after Musa Bilankulu was harshly penalised by referee Victor Gomes for a tackle on Donald Mokondelela in the area. Motshegwa scored on the follow-up after his re-taken penalty was saved by Goss.
Clinton Larsen's men showed intent at the restart, as Thembela Sikhakhane drew out a fine save by Masuluke Oscarine early into the second period.
However, Simandla made it 2-0 in the 75th minute, with the hosts dealt a further blow when Molefe was dismissed late on.
Arrows: Goss, Mngwengwe, Sikhakhane, Sibisi, Bilankulu (Hotto 68’), Ngcobo (Mahachi 38’), Molefe, Sibiya, Shitolo, Fikizolo (Mhango 49’), Sibeko.
Baroka: Masuluke, Ravhuhali, Nkabinde, Shaku, Mothwa (S Sangweni 26’), Ntsoane, Motshegwa, Simandla (Matete 90+2’), Chauke, Makgaka (Letsoalo 62’), Mokondelela.