Lucky Baloyi, Sifiso Ngobeni and Justice Chabalala made up Celtic's three changes from their clash against Bidvest Wits, while Sibusiso Hlubi featured as Rise and Shine's only alteration.
Celtic were first to pose a threat after Mzwanele Mahashe's looping header from a corner-kick before ten minutes was pushed over the top of goal by George Chigova.
Rise and Shine attempted to come alive following the earlier exchanges, but Kabelo Mahlasela as well as Zimbabwean international Charlton Mashumba was not able to work Celtic's defence.
Celtic launched a big scare following the 34th minute when Chabalala's header from a corner by Ndumiso Mabena cracked the top of the crossbar, with City beginning to live dangerously.
The visiting side turned attention to the bench at halftime and introduced Salulani Phiri for Dennis Chembezi in the heart of defence, with Victor Letsoalo hauled in for Celtic.
Siwelele Sa Masele survived an early scare to threaten from the back-post on 53 minutes through Andile Fikizolo's close-range strike following a cross-field ball, but Chigova palmed away.
Mashumba should've given Polokwane the lead seven minutes later following a near post header in the area off a cross, but the effort skied over the top.
Opportunities continued falling for Polokwane when Mpho Mvelase ran-in behind the defence on 68 minutes for a first-time strike from an acute angle, but Sipho Chaine parried successfully.
Celtic began finding the going tough following the final minutes as Rise and Shine continued to find openings, but the match culminated in a stalemate.
Celtic: Chaine, Letlabika, Mhahshe, Luthuli, Mabena, Chabalala, Sera, Fikizolo, Mashikinya, Baloyi, Ngobeni.
Subs: Mabokgwane, Ndou, Lingwati, Maema, Letsoalo, Tchilimbou, De Jongh, Maloisane.
Polokwane: Chigova, Nkili, Chembezi, Motloung, Buthelezi, Mvelase, Manaka, Nene, Mahlasela, Mashumba, Hlubi.
Subs: Phali, Maluleke, Semenya, Mngomezulu, Nku, Hlongwane, Anas, Tlolane, Phiri.