Having been well to wrap up the series in Dunedin - both before and after their collapse - it was another example of the belief, and depth, in England's one-day cricket. Bairstow, who was not opening the batting a year ago, and now has four centuries and on Saturday, he added 155 with Alex Hales, who had sat out the series until now and only played because of Jason Roy's back injury.
Nothing can replicate the pressure of a knockout game in a global event, but with teams now entering the final 12-month build-up to the 2019 World Cup, any kind of practice is useful. England made the most of it, New Zealand faded badly.
"We'd spoken many times about it being 2-2 and a huge game," Bairstow said. "The way the guys came out, people had compared it to a knockout game, and the guys said this is how we'll react. There was disappointment in the last game, huge credit to Ross for the innings he played, but that wasn't good enough from us. We knew we needed to get better in certain areas and put in a clinical, ruthless performance and that's what we did."
The ruthlessness was in no small part due to Bairstow as he crunched a 58-ball century, England's third-fastest, to follow his 138 in Dunedin. "I'm happy, really happy to be honest with you," he said. "After being in and out of the side, getting the odd game here or there, to then come in and contribute in a role I've not done a huge amount previously - you are still learning - is really pleasing. To score hundreds is your job."
And before the innings, Bairstow had taken a magnificent running catch around the deep midwicket boundary. "It's been a good day. Really pleased to hold a catch like that, around the boundary at full tilt and it's not far off your ankles. At first you aren't sure if you are getting there, you have a second or two to judge it. It's a split-second decision, sometimes you get it right."
Before the one-day series in Australia, Morgan had spoken about how he thought these two series would expose some of England's weaknesses so was delighted to come out with 4-1 and 3-2 victories respectively. They had the Australia series wrapped up after three matches, but in New Zealand, they had to come back from a match down and then face a decider.
"Reproducing things you do every day under pressure is something we do as professional sportsmen but doing it in a must-win game is that bit more important," Morgan said. "We haven't necessarily played our perfect game this winter but we've shown a lot of fight and character. We've won some games where, perhaps, we didn't deserve to win them and that's a really good sign for the team."
Morgan highlighted the bowling as the major area of gains over the last 10 matches and it was with the ball that England set the foundations for victory in Christchurch. Chris Woakes, who was named Man of the Series, did not go for more than 18 in any of his opening spells and again removed Colin Munro early in this match while Mark Wood claimed Kane Williamson cheaply too.
"I think the bowling has come on hugely, probably our biggest improvement this winter," Morgan said. "Defending a score without Liam Plunkett in Sydney or the Wellington match here. Never believing we are out of the game."
For New Zealand, this game had all but gone when they slumped to 93 for 6 in similar fashion to their defeat in Mount Maunganui, with the middle order struggling again in the absence of Ross Taylor.
"The disappointing thing today is that there were too many soft dismissals through that middle order, we failed to adapt on a surface that was a little soft to start and the ball stood up but it was a good surface," Williamson said. "There were definite decision-making errors on our part and that was the frustrating thing
"England were good throughout this series and they never gave us an inch and today."