England had smashed an awesome 241-3 in their 20 overs in the fourth Twenty20 worldwide at McLean Park in Napier on Friday evening.
New Zealand have brought back Boult for Lockie Ferguson as expected, and Daryl Mitchell replaces a slightly off-colour Jimmy Neesham.
Meanwhile, England's red-ball specialists have arrived in Auckland alongside Darren Gough, who will act as a consultant for the fast bowlers ahead of the two Tests.
Following the conclusion of the five-match Twenty20 global series on Sunday, Bairstow will stay for the two warm-up matches against New Zealand Cricket XI.
Matt Parkinson, who bowled only two overs on his worldwide debut in Nelson, retains his place ahead of Adil Rashid. "It looks a good wicket, It usually has a bit of pace in it here", said. Morgan also reasoned that, "a year down the road", the inexperienced side that stumbled to defeat from a promising position in Nelson would have won that game "nine times out of 10".
He suggested that, with the experience of Jordan and Bairstow, England were a strengthened side.
"Yorkshire and England batsman Jonny Bairstow has been added to the Test squad for the two-match Test series against New Zealand as back-up for the injured Kent batsman Joe Denly", an England statement said.
He got a full toss on the middle stump, but merely flicked to midwicket where Dawid Malan took a comfortable catch.