Parker started his second game this season having been a benchwarmer since returning from injury last month.
Parker’s goal in the first half saw Chiefs unbeaten in 12 matches, with seven matches in the PSL and five in cup games.
The Bafana Bafana striker scored with his chest following a cross from Sphiwe Tshabalala.
This 1-0 win at FNB Stadium was the second for Chiefs within a week after Chiefs beat the KwaZulu-Natal side by the same scoreline, a week ago today.
Amakhosi coach, Stuart Baxter, made a few alterations to starting line-up from the team as Morgan Gould, Kgotso Moleko, Reyaad Pieterse, Siyabonga Nkosi all started, having not played last week.
On the bench Baxter kept regular starters such as Eric Mathoho, Reneilwe Letsholonyane, George Lebese, George Maluleka and goalkeeper Brilliant Khuzwayo.
This showed some depth in the Chiefs side.
United did not impose themselves enough against Chiefs at Nasrec as the home side kept dictating terms throughout the game.