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The Kaizer Chiefs star netted twice in the final six minutes, first a wonderful free-kick from 25m, and then a penalty.
Having netted in each of Bafana's past four World Cup qualifiers, and scored five goals in all, Parker is now joint top scorer in the African section along with four other players though all the others will get the opportunity to add to their tally in the final round of qualifiers.
Parker was not selected by former coach Pitso Mosimane for the qualifiers against Ethiopia and Botswana in June last year. Bafana drew both matches.
It now leaves the 27-year-old with the possibility of chasing down the country's leading marksman, Benni McCarthy, who scored 31 goals in 80 international matches, though to do that he would need to rediscover the prolific form in front of goal that he displayed in the early part of his international career.
Parker took eight internationals to get his first Bafana goal, netting a brace in a 3-0 friendly win over Malawi in 2008, but then scored seven in his next nine internationals, including victories over Ghana and Cameroon, and the first in a 2-1 success against Norway.
Parker has not been helped at times by being played wide on the left rather than as a central striker, not that you would ever hear him complain about that.
He will have the chance to equal or overtake Phil Masinga in fourth spot on the all-time list when Bafana tackle Zimbabwe at Orlando Stadium tonight, the lanky former national team striker having netted 18 goals for his country.
Benni McCarthy - 31 goals in 80 internationals; Shaun Bartlett - 29 in 74 internationals; Katlego Mphela - 23 in 52 internationals; Masinga - 18 in 58 internationals; Parker - 17 in 60 internationals