Amelia Kerr’s career-best spell (4-20) had given New Zealand hope after Healy and Ellyse Perry (34 off 33) looked comfortable, the spinner knocking over Gardner then taking three wickets in her final over.
Phoebe Litchfield and Sophie Molineux took sharp catches to dismiss key pair Suzie Bates (34 off 34) and Sophie Devin (four off 10) and send Australia towards victory.
There were fumbles though. Megan Schutt dropped a sitter at point late in the game, while several run-outs went begging.
Perry’s dismissal was also forgettable, the allrounder taking off for a run after being struck on the toe, only for the wicketkeeper to whip off the bails.
The sides will complete their series at Brisbane’s Allan Border Field on Tuesday before departing for next month’s World Cup in the UAE.
“Probably not the prettiest, but those are pretty important wins to prepare us for what’s to come,” Australian allrounder Annabel Sutherland said.
“I’m pretty proud of the group; the way they stuck together with the ball and found a way to win pretty comfortably in the end.
“We didn’t quite get the total we were after but ... a win’s a win.”