Kayal Iro, son of Kiwis great Kevin Iro, ran in two of the Cooks' six tries; the Tongans only cut the chalk once.
Earlier, the Papua New Guinea men's team defeated the USA, 27-10.
Junior Vavai scored the opening try for the US before the former Hunters players Watson Boas, Edene Gebbie and Stargroth Amean ran in three of PNG's six tries.
Meanwhile, Samoa were too good for Fiji, winning 32-17.
Brian To'o scored two of Samoa's six tries; Fiji ran in three.
Today in Sydney, Samoa take on the Cooks, Tonga meet Fiji and PNG face New Zealand.