The two sides got off to a pretty even start with TS Galaxy striker Siphamandla Ngwenya missing a header from close range in the ninth minute from a Siphesihle Maduna cross.
The visitors then surged forward in attack with Thabang Matuludi missing a chance before Juan Mutudza slotted home from inside the box to give City a 1-0 lead.
City had the better of the opportunities heading into the first half but failed to add on to their lead until the 48th minute in the second half through a Juan Mutudza right footed shot into the top corner.
The Rockets then attempted to get back into the match with a barrage of attacks and were eventually rewarded when they breached a resolute City defence in the 81st minute through Igor Silva.
READ: Eric Tinkler admits Sekhukhune United face tough task in third-place chase
However, the home side could not find the equalizer, condemning them to their eighth Betway Premiership match without a victory despite their progression to the 2025/26 Nedbank Cup final.
The result sees Rise and Shine remain seventh on the log with TS Galaxy in 12th position.