The visitors lost wickets at regular intervals, as Parker dug into their batting order before helping topple Tembisa for 122 after 35.3 overs.
Alyus Pretorius notched up a further two wickets to his name, while Jean Rossouw and George Viviers claimed one apiece.
Sphamandla Dapo finished as his side’s highest scorer, with 46, while three of his teammates, Howard Harineki, Zwelo Ntsimbini and Rerat Naidoo, were all dismissed for a duck.
CBC only conceded two wickets in response as they marched to the 122 target.
Dylan Smalberger and Wickus Germishuizen, both finished with 22 runs, with Akshay Maharaj’s unbeaten 39 and Nicholas’ 37 not-out seeing CBC through.
Willie Bernhardt’s men travel to Benoni this weekend to face table-topping Northerns in a match that will go a long way in deciding the Premier League title, and the skipper is backing his troops’ chances.
“We obviously fancy our chances to beat them again. They have a good bowling attack with Lee Cothill bowling really well,” said Bernhardt.
CBC remaining fixtures:
Northerns v CBC – Sunday, February 22
CBC v KT Windies – Sunday, March 1
CBC v Kempton – Sunday, March 15 – @SabeloBoksburg
