The platform was well set for both to capitalise after Williamson's emphatic knock of 72 from 46 balls combined with opener Martin Guptill's 65 to ensure a sturdy foundation was laid for the middle order.
Malan, who finished with 59, started slowly, struggling to pick leg-spinner Sodhi's googly, but then accelerated nicely, hitting two sixes and six boundaries in 40 balls.
It was New Zealand's first win in two games while England are winless after three.
England have zero points and need Australia to do them a favour to take their chances of reaching the final into their last game against New Zealand on Sunday, 25 February.
England captain Jos Buttler said he wanted to see what his attack could do on an unpredictable looking drop-in pitch at Westpac Stadium that features huge bald patches.
A day earlier Williamson insisted he would continue playing all three formats for his country, despite a run drought in the shortest format and questions about the toll it was taking. Williamson was never going to miss out, scoring his singles then expanding, like a four from a misfield by Tom Curran subbing at extra-cover.
Williamson's maximums came behind square, straight down the ground, over deep mid-wicket and over fine leg.
Jordan also removed Williamson in an 18th over in which he conceded only three runs.
Liverpool cruise to win at Southampton to return to third place
Pellegrino said: "I think we have to be grateful with him and now we have to think that Virgil is part of the past". But it wasn't his goal that wowed the Liverpool fans, but his assist for Salah's first half strike.
Continuing their stand-out form from the domestic T20 competition, Auckland's Mark Chapman made a confident and composed 20 off 13 balls, while Northern Districts wicketkeeper Tim Seifert blasted an unbeaten 14 off just six deliveries in a critical late cameo to push the Blackcaps total just shy of the 200 mark.
Two wickets in consecutive balls in the 18th over from left arm swing bowler Trent Boult pushed New Zealand to victory in a thrilling T20 Tri-Series clash in Wellington tonight.
Unfortunately for England, Jordan's heroics weren't enough to stave off another T20 defeat for the Poms.
Let's look at the match highlights and important statistics.
Although, England took wickets regularly, Williamson kept powering on, hitting Plunkett and Wood over long off and midwicket respectively, reaching his eighth T20I half-century.
New Zealand should have put the game to bed earlier with Mitchell Santner and Tim Southee spilling easy balls.
'New Zealand had a lot of plans but I thought England looked a bit headless in the field with the ball'. "We dragged it back pretty well but they got too many", he said.