New Zealand didn't get the desired start at the Hagley Oval after losing Martin Guptill (2) early on.
England didn't allow the Kiwis to march on and kept pegging them back with wickets at key moments.
Ross Taylor (44) and Daryl Mitchell (30) shared a 56-run stand.
In reply, England maintained the composure.
Vince and Eoin Morgan (34*) shared a crucial 54-run stand.
England batsmen register these feats
Morgan increased his tally to 1,844 career T20I runs for England.
He hit four boundaries in the match to take his tally to 140 fours in T20Is.
Jonny Bairstow (35) surpassed former England batsman Craig Kieswetter (526) in terms of career T20I runs (548).
Vince registered his maiden career T20I fifty.
He also went past Dawid Malan and Moeen Ali regarding career T20I runs.
Santner surpasses Vettori, Jordan one wicket away from special feat
Chris Jordan (2/28) is just one wicket away from registering the feat of 50 scalps (49).
Only, Stuart Broad (65) and Graeme Swann (51) are ahead of him.
New Zealand's left-arm spinner Mitchell Santner (3/23) was the lone spark for his side.
He went past Daniel Vettori (38) in terms of T20I scalps (41) and needs three more to get past Kyle Mills (43).
England outsmart New Zealand in head-to-head tally
This was the 17th T20I match between the two sides. England registered their 10th victory against the Kiwis. This was also the eighth T20I played between the two teams in New Zealand. The visitors have a 6-2 advantage.