Suzie Bates and Amelia Kerr hit half-centuries as the White Ferns scored 162 for three on a slow pitch.
Sri Lanka could only manage 60 in reply.
Sri Lanka, who won their first two matches, finished the group stage level on points with New Zealand but were eliminated on net run rate.
Ms. Bates followed up her unbeaten 81 against Bangladesh on Friday with 56, while Ms. Kerr hit 66.
Bernadine Bezuidenhout set the tone for New Zealand, hitting 32 off 20 balls in an opening partnership of 46 in 5.4 overs with Ms. Bates.
Ms. Kerr joined Bates and the pair added 110 for the second wicket before Bates was stumped in the last over. Ms. Kerr was run out off the penultimate ball of the innings.
The New Zealand batters went for their shots and ran hard between wickets.
It was a performance that was in stark contrast to an earlier match on the same pitch when neither West Indies nor Pakistan could achieve a scoring rate of a run a ball.
Sri Lanka wilted under the pressure. Bezuidenhout and Bates were both dropped and there were numerous misfields.
Set to score more than eight runs an over, Sri Lanka’s chances evaporated rapidly.
They lost three wickets in the six-over powerplay before Amelia Kerr delivered a killer blow by trapping Sri Lanka captain and star player Chamari Athapaththu for 19 in the eighth over.
New Zealand used six bowlers and they all took wickets, with Lea Tahuhu and Amelia Kerr taking two each.
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