Bates blasted Pakistani bowlers to all parts of the ground while making a brilliant 168 of just 105 balls, while skipper Tiffen scored her maiden century to propel their team to a challenging total of 373 runs.
Both shared a record partnership of 262 runs. Their total was the third highest in Women's World Cups and the sixth highest overall in women's cricket.
Pakistan captain Urooj Mumtaz was left hapless by the Kiwi blitzkrieg. She used as many as eight bowlers in the innings. Mumtaz herself was the most expensive bowler as she gave away 20 runs in an over. While Naiila Nazir and Sajjida Shah grabbed two wickets apiece.
Pakistan made a valiant effort to chase, scoring their second highest total of the tournament, but went down by 223 runs.
They were bowled out for 150 in 48.1 overs.
For Pakistan, Nain Abidi scored 52 of 104 balls.
Pakistan will now face West-Indies for a fifth-place playoff.
The final will be played between New Zealand and England on Sunday.