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 back foot, from where they never recovered.
"It was very important for us to get a win tonight and some individual performances to go with that," England captain Stuart Broad said at the post-match presentation ceremony.
"First Steven Finn set the tone for us fantastically with the new ball and then obviously Luke Wright and Eoin Morgan batted beautifully as well.
"(Pitch was) Lot drier. We knew that from ball one. So it did turn a little bit. We are obviously delighted to have won today and we have got a huge game coming up on Monday now.
"We have got a job to do and hopefully try and build on the positives from tonight. There are areas to improve as well."
Left-hander James Franklin (50) hit some lusty blows towards the end of the innings to prop up New Zealand after they were reduced to 67 for four wickets at one stage.
The Black Caps, who play West Indies on Monday, are now on the brink of elimination, having lost both their Super Eight matches to Sri Lanka and England.
"I think 150 was probably a par total. It was quite hard to start on that wicket," captain Taylor said.
"I thought James' batting was outstanding to get us to that total. We were looking at getting 130-135 at one stage."
England, who lost to West Indies in their first Super Eight match, will play hosts Sri Lanka on Monday at the same venue.
