New Zealand posted 220- for eight in their 50 overs against England, with Amy Satterthwaite following up her century against the same opposition two days previously with 85 from 95 balls.
She didn't really find any significant support, with four players achieving scores of 20 or more , and in the end they were about 30 runs short of a challenging total.
Bates chipped in with 21, taking her overall tally for the tournament to 401 runs at an average of 67.83, and she still holds an 82-run lead over Stafanie Taylor (West Indies) as the tournament's leading runscorer.
England were largely comfortable throughout their chase thanks to an unbeaten 106 from English captain Charlotte Edwards who scored a record-equalling eighth one-day international ton in what might be her last World Cup game.
Sarah Taylor (26), Lydia Greenway (31) and Arran Brindle (27) helped England to 199-3 and, although they lost three wickets in three runs, cruised to the target with three overs to spare.
Opening bowler Sian Ruck was tidy with 2-20 off her 10 overs and Lucy Doolan finished with 3-50.