The 1.90-metre veteran is renowned for his aerial menace and when Stars crossed the ball on 83 minutes, Rodgers soared to nod powerfully past Zimbabwean goalkeeper George Chigova.
Ghana-born former Free State Stars forward Mohammed Anas had put Polokwane ahead on 62 minutes, scoring from inside the box despite being surrounded by three defenders.
Hosts Stars deserved a point as they dominated possession and territory only to fall victim to the common South African problem of poor finishing.
"We create plenty of chances from set pieces, but not enough from open play," admitted Serbia-born Free State Stars coach Nikola Kavazovic.
"My players hold on to the ball too long and go round in circles with it instead of pushing forward."
Jozef Vukusic, the Slovak coach of City, accepted a draw after a seven-hour bus journey from northern city Polokwane to central town Bethlehem.
He preferred to marvel at Rodgers' goal than talk about his team, who rose one place to sixth, seven points behind leaders Orlando Pirates with a match in hand.
"Rodgers is so tall and strong and very dangerous when the ball is crossed accurately to him. It was a great goal."