England, who had slumped to 138 for seven, finished on 209 for seven with wicket-keeper Nixon 42 not out and Plunkett unbeaten on 29.
Nixon faced just 41 balls with five fours while paceman Plunkett's 34-ball stay featured a straight six off left-arm spinner Daniel Vettori.
However, England may still not have enough runs to play with.
Kevin Pietersen, in his first full international since January after sustaining a rib injury during the Australia one-dayers, top scored with 60 but then got himself out.
From 133 for three, England lost four wickets for five runs with the worst part of the collapse seeing three go down for one run in seven balls as key batsmen Paul Collingwood (31), Pietersen and Andrew Flintoff, out for a first ball nought, all fell in quick succession.
Fast bowler Shane Bond, who finished with two for 19 off his full 10 overs, took two wickets in four balls as Pietersen tamely holed out to James Franklin at long-on before Flintoff chipped to Scott Styris at short cover.
Styris (two for 25) had started the slump when, two balls after dropping Collingwood off his own bowling, he saw an attempted guide to third man well-held by Brendon McCullum - one of four catches for the wicket-keeper.
Pietersen and Collingwood's fourth-wicket stand of 81 was the best of the innings but, with New Zealand captain Stephen Fleming's bowling changes often yielding a wicket, the Black Caps were on top for the most part.
Fleming, on a pitch freshened by early morning rain, which delayed the start by 30 minutes, saw his decision to field first quickly rewarded when left-arm quick Franklin struck with the day's second ball when Irish-born Ed Joyce was caught behind for nought after slashing outside his off-stump.
First change Jacob Oram took a wicket with his fifth ball when Ian Bell (five) edged behind after advancing down the pitch.
England's 30 for two in the ninth over almost became 32 for three in the 11th when Pietersen went for a risky single to get off the mark.
Vettori quickly threw from mid-off to the far end where Vaughan, on 20, was yards out.
But McCullum failed to gather and the England skipper, battling a hamstring injury that saw him play just three games in his side's victorious tri-series campaign in Australia concluded last month, survived.
Vaughan's mini-repreive didn't last long, Franklin bowling him for 26 after he bottom-egded a pull into his stumps.
Pietersen, after rebuilding with Collingwood, opened up with a six over long-on against off-spinner Jeetan Patel before completing a 73 ball-fifty also featuring four fours.
England and New Zealand - who beat each other twice in Australia - are firm favourites to qualify from a group also featuring Kenya and Canada.
Assuming both Test sides do go through, the winners of this match will carry forward two points into the second phase, Super Eight stage.
England 209 for 7 in 50 overs (Pietersen 60, Nixon 42 n o, Collingwood 31, Plunkett 29 n o; Bond 2 for 19, Styris 2 for 25, Franklin 2 for 43) Vs New Zealand (yet to bat).