Wright, who made 99 against Afghanistan in the group stages, hit five massive sixes and an equal number of boundaries and added 89 runs for the third wicket with Eoin Morgan (30) as England reached their target of 149 with seven balls to spare.
New Zealand spinners Daniel Vettori and Nathan McCullum dismissed the openers cheaply to put England's chase under pressure but the partnership between Wright and Morgan shut them out of the match.
England paceman Steve Finn picked up three wickets for 16 runs as New Zealand were restricted to 148 for six after captain Ross Taylor won the toss and opted to bat first.
The lanky seamer dismissed the dangerous Martin Guptill and Brendon McCullum in his first spell to put New Zealand on the backfoot from where they never recovered.
Lanka thump Windies
Hosts Sri Lanka outsmarted the West Indies by nine wickets to move one step closer to a semi-final berth after winning their Super Eights group one match at Pallekele stadium on Saturday. Sri Lankan spinners kept the West Indian big hitters to 129-5 in 20 overs before chasing the modest target in the 16th over for the loss of only one wicket to record their second win in the round of eight teams.
Mahela Jayawardene led the Sri Lankan reply with an unbeaten 65, sharing an unbroken 108-run stand for the second wicket with Kumar Sangakkara (39 not out). Sri Lanka must avoid defeat in their last match against England while the West Indies need to beat the Black Caps with a superior net run-rate.
Brief scores: WI 129-5 (M. Samuels 50) lost to SL 130-1 in 15.2 ov (M. Jayawardene 65 n.o.)