Essex left-arm seamer Topley and Hampshire batsman Vince join fellow T20 international newcomers Sam Billings, David Willey and Mark Wood in the squad for the one-off match on June 23.
Billings, Willey and Wood are all currently involved in the five-match one-day international series against New Zealand.
Eoin Morgan will captain the side but there is no place for former England T20 captain Stuart Broad.
"This match against New Zealand allows us another opportunity to look at players relatively new to international cricket as we look to build a squad for the World T20 in India this winter," national selector James Whitaker said on the ECB website (www.ecb.co.uk).
"The squad is made up of players who have demonstrated their ability in domestic cricket and fully deserve a chance to continue their progress against a very good New Zealand side.
"We have already seen our limited overs cricket begin to move in the right direction which is exciting but we are all aware that we have plenty more to do if we are going to challenge the very best sides in the world on a regular basis."
England and New Zealand are currently tied 2-2 in a pulsating ODI series, with the decider to come in Durham at Chester-le-Street on Saturday.
England squad: Eoin Morgan, Sam Billings, Jos Buttler, Steven Finn, Alex Hales, Adil Rashid, Joe Root, Jason Roy, Ben Stokes, Reece Topley, James Vince, David Willey, Mark Wood.
(Reporting By Michael Hann; editing by Amlan Chakraborty)
