Brook (43 not out off 27 balls) and Malan (54 off 42) shared a 54-run partnership on Wednesday as England reached their target of 140 with six overs to spare at Chester-le-Street for a seven-wicket victory.
England's selectors surprisingly left Brook out of the squad for the 50-over World Cup in India starting in October but his form is making a mockery of that decision.
Widely viewed as one of the world's most destructive batsmen, he starred in the recently completed edition of The Hundred and was devastating against New Zealand in hitting three sixes and two fours.
"He's been unbelievable, I'm fortunate enough to spend quite a bit of time with Harry on and off the field as well, I get on well with him," T20 international debutant Brydon Carse said of the Yorkshire batter.
"To see him go about his business over the last 18 months has been a joy to watch, he's such a laid back character in and around training, he loves batting."
Malan got a much-needed big score after some patchy recent form, reaching fifty for the 16th time in T20 internationals and helping to steady the innings after the early loss of Jonny Bairstow (four) in England's reply to New Zealand's 9-139.
Liam Livingstone (10) got England over the line with a huge pull for six, while Jos Buttler, England's captain and star batter, wasn't even needed to bat.
Malan and Livingstone are in England's World Cup squad and Brook is putting huge pressure on selectors to get the call, too, with the group heading for India not having to be finalised until the end of September.
Put in to bat, New Zealand's Glenn Phillips was the visitors' top-scorer with 41 off 38 balls but the Black Caps struggled after losing three wickets in 12 balls from 0-25.
Pace bowler Carse had 3-23 off four overs while Luke Wood, who was hit for three sixes by Finn Allen (21) off the first over of the match, had figures of 3-37.
"I couldn't have asked for a better start," Carse said.
"Over the last year I've had massive ambitions to play for England.
"When I got the news from Jos (Buttler) yesterday afternoon that I'd be playing there was a lot of excitement to play at Durham, where I've played my cricket over the last nine years.
"So a lot of familiar faces and a lot of familiar surroundings, it probably just made me that little more relaxed coming into the game."
The second match of the series is in Manchester on Friday.