The Ferns innings was led by Rachel Priest and Katey Martin, who both made 77.
Priest made 50 from 51 balls but could manage only 27 from her next 50, but Martin continued a fantastic series with another aggressive knock to put the hosts in control.
Her innings was of extra value after Amy Satterthwaite, who had averaged 187.3 in her last five ODI's, was bowled sweeping for 11. However, Priest's best innings of the series, and another strong cameo from Katie Perkins (34 from 32), supplemented Martin's efforts to set the White Ferns up at 230-3 with just over seven overs remaining.
Fittingly, it was Lanning who halted their progress, taking a superb diving catch at mid-off to dismiss Martin, after which the Ferns stuttered.
They could make just 40 runs from their last seven overs, with a steady flow of wickets slowing what could have been a record total to chase.
Beth Mooney flew out of the gate in response for Australia, bringing up a 47-ball 50 as Australia once again started strongly, easing through to 108-1.
Seamer Holly Huddleston kept the Ferns alive, taking 3-44 from her 10 over spell, but she couldn't get wicket-taking support, and the Ferns struggled to find a consistent fifth bowling option.
Australia saw off promising spinner Amelia Kerr, who went for just 31 from her 10 overs, and then attacked her counterparts, with Lanning playing the leading role. She was at her best against the trio of Lea Tahuhu, Suzie Bates and Erin Bermingham, who bowled 23 wicketless overs and conceded 159 runs.
A 20-ball spell which saw two wickets fall for just two runs provided a testing time for the visitors, but Lanning got support from Elyse Villani (37 from 42) and Alex Blackwell (32 from 35) to stay in touch with the required run rate.
New Zealand had their chances to dismiss Lanning, with wicketkeeper Priest dropping a difficult chance off Bates' bowling, before missing a stumping chance from Kerr. During the stumping chance, a bail was dislodged, but the umpires ruled Priest had knocked it off, rather than the ball.
Making the most of those opportunities, Lanning brought up her 10th ODI century with three overs to go, and Alyssa Healy joined her to blast 21 from 16 balls.
Healy hit the winning runs with three balls to spare, and Lanning was at the other end to celebrate a deserved series victory.