England selectors have also recalled fast bowler Mark Wood, while batsman Liam Livingstone has been named in the Test squad for the very first time.
"People are saying that Test cricket's becoming less important, but as players I don't think that's true at all". Stoneman has had less opportunities but he too needs a big score in New Zealand to cement his place as Alastair Cook's opening partner.
"Liam has been a player that we have been impressed with for quite some time, having performed well in the county system with Lancashire and over the past couple of years with the England Lions", said England National Selector James Whitaker.
"During the recent Lions tour of Australia, he was a standout performer and showed a lot of maturity in his attitude and put in some strong performances".
Opener Mark Stoneman and No 3 James Vince both survive the axe, although they had modest returns against the Aussies.
Gary Ballance, Jake Ball and Tom Curran were the only absentees from the group of players led by captain Joe Root in Australia.
His participation in both still depends on the outcome of his legal case with Britain's Crown Prosecution Service which is still considering whether he should be charged for his alleged part in a street fight in Bristol a year ago that has prevented him from playing for England since.
"Some of the guys have been out here playing in the Big Bash, lads have been all over the world playing, so we're full of confidence and looking forward to that first game". Ball played in the first match at the Gabba and then was not seen again while Curran, a late call-up, was ineffectual in his two Tests at the MCG and SCG.
The 28-year-old's figures of 0-68 do not tell the story of a performance which showcased genuine speed, a commodity England's bowling sorely lacked during their 4-0 Ashes humbling.
Liam Livingstone, England's uncapped selection for the Test tour of New Zealand in March and April, believes he is better placed to impress in red-ball than white-ball cricket, after missing the chance to establish his credentials in two T20 appearances against South Africa last summer.