Cawthorne chased 172 for a four-wicket win at Tickhill.
Mustafa Shinwari took four wickets and Naqeebullah three.
Cawthorne went out of the Twenty20 Blast on Sunday.
They were out for 146 chasing 198 against Wickersley.
They won by nine runs against Doncaster after posting 178.
George Booth made 68 off 49 balls and Naqeebullah took three wickets.
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