Parris, who returned to the Women’s Super League from French side Lyon to sign for the Gunners earlier this summer, was joined on the scoresheet by fellow England forward Ellen White, who scored twice.
The match took place behind closed doors at the Todoroki Stadium in the Greater Tokyo area.
Hege Riise’s GB side had been scheduled to face Zambia in a warm-up match at Stoke’s bet365 Stadium on July 1, but the fixture was cancelled with the African team having to pull out because of complications linked to coronavirus restrictions.
GB are set to begin their Olympic campaign by facing Chile in Sapporo next Wednesday, then take on hosts Japan at the same venue three days later before concluding their group fixtures with a July 27 clash with Canada in Kashima.
New Zealand’s group also features the United States, Sweden and Australia, while the other pool consists of Holland, Brazil, China and Zambia.