Parker scored in first-half added time before he doubled the lead four minutes after the restart of the second half.
Njabulo Ngcobo, who scored an own goal to deny his side a clean sheet as they recorded a second consecutive PSL win after the initial 4-0 win over Chippa United, came under criticism as Parker was defended by the fans.
Stuart Baxter, a former SuperSport United head coach, gave an analysis of his current side as Parker enjoyed good moments and was later voted man of the match, as he explained what they have to do in order to keep performing.
"What we are is, we are very good at times when we do the job properly. We switch off too often, we lose our concentration, we lose our belief a little, and we have got to get rid of that," said the coach.
"We are slowly getting rid of that. And the results are showing that. So if the lads keep going, then win, lose or draw, I'll back them."
This is how Twitter reacted after Parker's brace:
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