City were full of attacking and looked enterprising but found little space to maneuver as a stingy Baroka applied a good block on them and thwarted their efforts, to the increasing frustration of the home support.
Putsche attacked another corner, again knocked in by Ayanda Patosi, and came close to breaking the deadlock after 37 minutes.
But the goal eventually came on the stroke of half-time as Thabo Nodada set up a surging run, played it out to Ebrahim Seedat who whipped in a perfect cross that Mthembu headed in off the post and seemingly over the line for a goal.
But goalkeeper Elvis Chipezeze scooped it out of the goal, straight to Patosi who had the easiest of tuck-aways.
Replays showed the ball had crossed the line. However, it was not quite clear who was the goal scorer and the Premier Soccer League will have to decide, with hindsight, whose goal it is.
It will be important as it is either the sixth goal of the season for Mthembu or fifth for Patosi, not far behind Golden Boot race leader Mothobi Mvala of Highjands Park.