The two sides got off to a pretty even start with 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.
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.
Abdeslam Ouaddou reserved special praise for Relebohile Mofokeng following the youngster's standout performance for Orlando Pirates but maintained that individual brilliance must always serve the team's collective goals.
Kaizer Chiefs are reportedly setting their sights on strengthening their squad ahead of next season, with highly rated ZESCO United midfielder Luka Mutoshi emerging as a potential target.
New Marumo Gallants head coach Jamil Benouahi admits his side made a number of mistakes in their 3-0 Betway Premiership loss to Magesi.
Durban City coach Pitso Dladla has defended his defensive tactics following a narrow 1-0 defeat to Betway Premiership title-chasing Mamelodi Sundowns on Tuesday.
