Yoan Gouffran's first-half goal proved to be enough to give Newcastle their second win on the tour after overcoming Sydney FC earlier in the week.
Wellington, who beat West Ham on Wednesday, matched Newcastle for long periods of the game with chances few and far between for both sides.
Newcastle grabbed the only goal of the game four minutes before the break when Gouffran got on the end of Vurnon Anita's cross to head home.
Rob Elliott ensured Newcastle held on for the victory in the second half as he made two fine stops to keep out efforts from Wellington's Jeremy Brockie.
The only negative for Alan Pardew were the injuries to Fabricio Coloccini and Siem De Jong as both players were forced to limp off at the Westpac Stadium with knocks.
Gouffran told Sky Sports News: "We are very happy to win the game and we are very happy to get this (Football United) trophy. This is good for the confidence.
"It's good for the fans from New Zealand, it's good for us to win new fans in the world; we are happy to come here. We have to be ready for the start of the season and we will work very hard on the training ground and we will be ready."