Malan made a 114-ball 127 with 14 fours and three sixes to lay the platform for a strong 9-311 in 50 overs, after Jos Buttler won the toss and opted to bat on Friday, with the visitors only managing 211 in response.
To complete a miserable day for the Black Caps, key seamer Tim Southee suffered a fractured hand in the field which could threaten his World Cup participation.
Needing a win to avoid defeat in the ODI series, New Zealand got off to a poor start as they lost opener Devon Conway cheaply following an excellent run out by Buttler.
Henry Nicholls (41) gave the visitors a glimmer of hope but incisive bowling by Moeen snuffed out the threat, though the spinner was denied a hat-trick on his way to figures of 4-50.
All-rounder Rachin Ravindra led the scoring for New Zealand as he valiantly battled on until the end, hitting 61 off 48 balls, but his resistance was ended by Sam Curran's excellent yorker.
Southee's broken hand meant New Zealand were one batsman short when their innings came to an end on 211 in the 39th over.
"When you're faced with those challenges, it's important for guys to step up. Southee's in good spirits. He'll be assessed further to see how he is. Fingers crossed," New Zealand captain Tom Latham said.
Earlier, Malan was the cornerstone of England's innings and was involved in three significant partnerships.
He added 79 with Joe Root (29), 56 with Buttler (36) and 48 with Liam Livingstone (28), before departing on 127 when he nicked a Ravindra delivery into Latham's gloves.
"Good run, especially scoring some runs here at the home of cricket and leading into a World Cup. It was a bit slow, when they built pressure I found it hard to score," Malan said.
"But we built partnerships and got up to 300, which it what we were aiming for... Trying to break into this team, you either have to be a freak or be consistent, and that's what I've tried to do, put match-winning performances on the board."
Captain Buttler said of the series: "We got better and better. We wanted to play our style of cricket and we were true to that. We had to get off to a good start with the ball and we did that."
Butler said he believed the champions were in a good position to defend the World Cup.
"We're building nicely to go there and win. It's an exciting time."
Ravindra was the pick of New Zealand's bowlers, claiming the wickets of Malan, Root, Harry Brook and Moeen to limit the damage.
Buttler's side next take on Ireland, while New Zealand face Bangladesh.
The teams will then meet in the opening match of the 50-overs World Cup in India on October 5.