Rise and Shine, who came into the game on the back of seven straight defeats across all competitions, missed striker Puleng Tlolane and defender Mpho Mvelase through suspension.
The duo's absence was felt as early as the ninth minute when Ndumiso Mabena shaved the top of the crossbar with a low header from a cross by Sifiso Ngobeni.
Siwelele, who won the corresponding fixture with the last kick of the game last season, start to the match signalled another triumph over City who struggled to hit first gear.
Neo Maema and Victor Letsoalo were the game's first changes as Lehlohonolo Seema went for the kill right after the halftime interval.
Cyril Chibwe continued standing tall for the visitors towards the last 20 minutes, after palming Mzwanele Mahashe's header for a corner following a floating delivery into the area.
Bernard Molekwa issued his first change within three minutes as Lesiba Nku made an entry for Mngomezulu, with Siwelele searching on all fronts for the opener.
Rise and Shine banked on Charlton Mashumba, the man with the league's only hat-trick this season, but the Zimbabwean fired blanks from the few openings that came his way later on.
This had Polowane's fate sealed when a one-two on the edge of the area between Mabena and Letsoalo saw the latter firing through the on-rushing Chibwe with nine minutes remaining.
As a result, Siwelele return to winning ways to go fifth following back-to-back draws, while City suffer an eighth straight defeat.
Polokwane: Chibwe, Nthatheni, Hlongwane, Nene, Motloung, Manaka, Mashumba, Maluleke, Mngomezulu, Phiri, Hlubi.
Subs: Chigova, Anas, Sikhondze, Buthelezi, Maluleke, Chauke, Nku.
Celtic: Mabokgwane, Mashikinya, Ngobeni, Baloyi, Pdumidzai, Masuku, Luthuli, Sera, Mahashe, Phalane.
Subs: Mpoto, Matjila, Letsoalo, Tani, Khasipe, Meama, Maloisane.