But for a couple of hundreds from the nettlesome Ross Taylor, in Hamilton and Dunedin, they might well have done, Taylor inspiring victories in the first match and also in the fourth.
Injury prevented Taylor from playing in Christchurch, where the series was poised with the score 2-2.
It gave England the perfect chance to show that they can perform under pressure before next year’s World Cup, and, inspired by a second successive hundred from Yorkshire’s Jonny Bairstow, who reached the landmark from just 58 balls, they grabbed it with both hands, winning by seven wickets with 17.2 overs to spare to seal their sixth ODI series victory on the bounce.
In many ways, England will go into that World Cup on a hiding to nothing of their own construction.
Not only are they the host nation, but also a team totally transformed from the previous World Cup, where they suffered an embarrassing early exit.
England will be expected by many to lift the trophy on the back of their continued excellence in the one-day game, which is winning admirers at home and abroad.
By common consent, the only question is whether they can summon the strength to get over the line in key knockout fixtures, having lost in the Champions Trophy semi-final last summer, for example.
As ever, the proof of the pudding will be in the eating, but anyone who cannot admire the way that England are playing their one-day cricket at present has little concept of the majestic.
It was summed up in Christchurch by the brilliant Bairstow, who followed his 138 in Dunedin with an innings of 104 from 60 balls, exactly one-quarter of which he sent to the boundary in the form of nine fours and six sixes.
After New Zealand were dismissed for 223, Adil Rashid and Chris Woakes each taking three wickets, Bairstow blasted the third-fastest one-day hundred in England’s history, behind Jos Buttler (off 46 balls) and Moeen Ali (53).
It was his fourth ODI century in the past six months as an opener, following a brace of tons against the West Indies, and it was the second successive time that he had clinched a one-day series against New Zealand, having struck an unbeaten 83 when the sides met in another decider at Chester-le-Street in 2015.
By dint of sheer hard work, skill and a refusal to give up, Bairstow has become an indispensable member of England’s one-day team and now averages close to 50 in the 50-over format.
Having initially struggled to hold down a place, due to the inability of others to detect his talents rather than through any fault of his own, he is a match-winner now on a potential collision course with a World Cup winner’s medal, although neither he nor his team-mates will be taking anything for granted.
Bairstow’s brace of centuries against the Kiwis were as good as anything you will see from a man who deserves to be ranked as one of the best and most versatile batsmen in the world.
Indeed, Bairstow could surely bat in any position in any format, keep wicket in any format, and, as he showed in Christchurch, he can also turn it on in the outfield too, his running, one-handed diving boundary catch to remove Tim Southee emphasising that he is very much the complete all-round package.
If Bairstow made mincemeat of the run-chase, before inadvertently hitting his own stumps as he tried to attack Trent Boult, then Alex Hales was an excellent foil.
The Notts man contributed 61 to their rollocking opening stand of 155 inside 21 overs, with Hales taking his opportunity after a back spasm ruled out Jason Roy.
While Bairstow led the way, peppering all corners of the picturesque Hagley Park, Hales played the role of harmonious second fiddle.
It was a near-perfect performance by Eoin Morgan’s men, for whom man-of-the-series Woakes set the tone with the ball.
Afterwards, Bairstow described the display as “ruthless”, which was as good a word as any.
He also said that he is “still a work in progress” as he attempts to make more big hundreds and match-winning scores.
It highlights the level-headed attitude of a player who is simply enjoying his cricket for all he is worth and playing the game with a smile on his face.
As the man himself put it: “It’s great fun.
“Any time you go out to play for England in an amazing country you are very fortunate to travel to, it’s something you have to go and enjoy.”