Hawkes Bay pitcher Courtney Gettins suffered the loss, allowing six hits and six runs, with two strikeouts in her 2.1 innings.
Aucklander Beth Stavert replaced Gettins in the third inning and pitched five strikeouts without further scoring.
Cooper was New Zealand's best batter, with two hits, a run and another batted in from her four appearances.
With Venezuela's withdrawal, the Kiwis benefited from a forfeit and now have a 2-1 record, with matches to come against unbeaten United States, Korea and Canada.
At 3.30am tomorrow, they face Czech Republic - who were 13-0 losers to USA today - and then the Koreans at 9am.