Puleng Tlolane netted the decisive goal on 32 minutes as City got their season up and running on the road.
A lively opening quarter saw Polokwane with a handful of chances, but a lack of composure saw them squander their first real opportunity in the 13th minute.
Thabo Mnyamane, at the other end, had his shot easily stopped by City's new goalkeeper Dino Visser.
Where Mnyamane failed, Tlolane succeeded as the nuggety striker slotted home following a clinical set of touches which sent the attacker free on goal and primed to take full advantage, which he did, curling his shot into the bottom right corner.
City came out after the interval looking content to defend their slender lead, which rarely looked under threat.
Tuks coach Steve Barker made two changes after the break, bringing on Khethukuthula Zwane and Lucky Mathosi after an hour, with the pair making inroads after their inclusion.
Mathosi made a nuisance of himself deep in the Polokwane area but missed a fine chance when he headed high and wide of the mark in what looked to be Tuks' best chance of the second stanza.