Southee's figures of four for 38 took New Zealand to the brink of victory as England, chasing just 183 to win, were bowled out for 160.
The 19-year-old was responsible for a middle-order collapse that saw England lose three wickets for no runs in eight balls as they slumped to 64 for six.
He then returned to have Paul Collingwood lbw for a top score of 34 when the England captain looked as if he might win the game off his own bat.
New Zealand, bowled out for 182, were indebted to all-rounder Grant Elliott, who top scored with 56 in only his second match at this level and a rapid, career-best 47 from man-of-the-match Kyle Mills.
It was another impressive effort by the 29-year-old South Africa-born Elliott who took took three for 23 on debut during Wednesday's controversial no-result at Edgbaston following his call-up into the squad last week from south-east English club side Weybridge.
And medium-pacer Elliott finished the match with 22 balls to spare when Chris Tremlett skied to New Zealand captain Daniel Vettori.
Collingwood put on 65 for the seventh wicket with Graeme Swann in 17 overs.
But when Swann clipped Scott Styris to Ross Taylor at mid-wicket for 29, England were 129 for seven, still needing 54 more runs to win and without a frontline batsman at the crease the target was beyond them.
England were making progress when Southee, in only his third ODI, struck.
Ravi Bopara went for 27 when a cut was well-held by a diving Jamie How at backward point before the dangerous Owais Shah fell for a three-ball nought, undone by a good length delivery which bounced and was caught by Styris at second slip
Tim Ambrose also exited for a 'duck', Taylor holding a first slip chance at the second attempt.
Earlier, New Zealand's scored 50 runs off their final five overs, with paceman James Anderson conceding 18 runs off his last.
Mills's runs came off just 40 balls with two sixes and five fours.
As a result England, who saw fast bowler Stuart Broad take two for 14 in an unbroken 10-over spell, had to chased a much bigger total than looked likely when New Zealand slumped to 49 for five
Elliott faced 102 balls with three fours before he was caught by Luke Wright after hooking Anderson.
England's reply began shakily when Mills removed Wright and star batsman Kevin Pietersen to leave them 19 for two.
Dashing Kiwi opener Brendon McCullum took 16 runs off the first five balls off the third over, from Anderson, including a six flicked over square leg.
But off the sixth ball he was well caught by a leaping Pietersen at mid-off going for another big shot.
England then put the brakes on by taking three wickets for five runs in 17 balls to leave New Zealand 42 for four.
How bottom-edged a pull off Broad into his stumps before Styris gloved a rising ball from Tremlett, a replacement for dropped Hampshire colleague Dimitri Mascarenhas, through to wicket-keeper Ambrose.
Broad struck again by bowling Taylor, who played round a straight ball.
Mills smashed Anderson for six and cleared the ropes again off Wright before he was out off the last ball of the innings.
The series continues on Wednesday at The Oval.