The Kiwis then took advantage in defence of the Aussies' predictability in the attacking circle as they seemed bereft of ideas to create scoring opportunities.
It was the Sticks who had lateral vision, cohesiveness and superb direction from Stacey Michelsen in the engine room.
Flynn missed a golden opportunity in the 31st minute to increase the margin, albeit from a tricky pitch-wedgelike ball in front of a gaping goalmouth.
But the Ockers levelled terms 1-1 in the 39th minute through striker Emily Smith from a reloaded penalty corner (PC).
Brooke Peris made it 2-1 from a field goal in the 43rd minute after Smith became provider.
That stung the Kiwis into action and Olivia Merry struck within a minute of the end of the third spell to make it 2-2.
That last quarter was always going to be about character and that unmistakable never-say-die Aussie mental fortitude came through.
Said Hager: "Look, it was our errors ... we rushed out to make an intercept which we didn't need to do ... but then again you make mistakes then you have to cover up to make sure they don't score goals.
"I think the disappointing thing is they got a [penalty] corner with 15 seconds to go or whatever ... I'm not sure if it was a corner [because] I need to look at the video footage," Hager said, ruing his troops missing an opportunity on attack.
It could have gone either way, he lamented, but emphasised his players needed to learn to win those games.
Australian Hager was in no mood to entertain to "take the positives" view to camouflage their inability to go for the jugular when the stakes become higher in the playoffs.
"Oh yeah, yeah but one of the goals for this team in this tournament was to win it and it wasn't to come second, third or fourth so now we haven't reached our objective which means we have to go away now and become better again."
Michelsen, who has more than 170 caps, was the star.
"I thought she had a blinder tonight and she was probably a little unlucky not to score a couple of goals."
Hager felt the Kiwis were in line for a couple of PCs at the death but the video referral system was "pretty redundant".
"That's life so you have to put up with that."
Asked if he would like to see it introduced here next year, he replied: "Look you always want to see it because it's at the majors but you have to give Australia credit because they fought back and got the win in the end so we've got to get better next time."
His focus now turns to selecting a team for the Olympic qualifiers in three weeks.
"We don't have some players here so we have to look at in the camp in May before we make our final selection."
Former captain Kayla Whitelock (nee Sharland) is expecting her first baby in a fortnight and most-capped female Black Sticks player Emily Naylor is on a break, but Hager said it would be nice to have them back for the Rio Olympics next year.
"It was good to have Anita Punt's 200th [game] but it's just unlucky we couldn't come away with a win."
Aussie hero Kenny said it felt great to score the winner, although it was just behind the goal she scored in the Glasgow Commonwealth Games.
"We had a bit of a slow start and let in an early goal which was a bit disappointing but we stuck to the process and kept pushing right to the end," the beaming 28-year-old said.
"We're really happy with the win but we have a lot to work on but at times a win's a win," she said, agreeing the Kiwi midfield had bullied them.
The first equaliser came as a relief but the victors also sensed blood to go ahead but hailed the Kiwis as great opposition.
Coach Adam Commens reiterated the need to "stick to the processes" in any game.
"We weren't executing our objectives so well in the first half and the Black Sticks played very well so I was satisfied our girls sticking to their guns ..." he said, adding they got a good snapshot of development.
