Katey Martin and Sophie Devine had helped New Zealand to a more than competitive 162 with a burst in the final four overs.
Then Devine got rid of Alyssa Healy and Elyse Villani in the same over, while Beth Mooney and Ashleigh Gardner also fell swiftly. The home team were reeling at 45 for 4.
But Australia were determined to keep their unbeaten record at North Sydney Oval.
Haynes played the role of the aggressor while Lanning gave her excellent support. The New Zealand captain, Amy Satterthwaite, had no answer to the Australian pair.
The Australian duo built their chase perfectly. They were steady initially but finished with a flurry of boundaries and in the end Australia romped home with 14 balls to spare and six wickets in hand.
Lanning remained unbeaten on 56 in just 44 deliveries while Haynes was unbeaten on 69 off just 40 deliveries. The pair added a match-winning unbeaten stand of 119.
Sophie Molineux was the most restrictive Australian bowler conceding just 21 run in her four overs.
This match was the first televised international on Australian soil not broadcast by Channel Nine in almost 40 years.
First Published: September 29, 2018, 9:38 PM IST