After Southee almost single-handedly skittled England for 123, captain Brendon McCullum bludgeoned 77 off 25 balls - making the quickest World Cup half-century (18 balls) - as New Zealand completed a rout.
Swing was the key to all of Southee's dismissals - four of which came via him hitting the off-stump - as he decimated Eoin Morgan's hapless side.
Joe Root (46) provided some resistance for England, who were bowled out in the 34th over, before the Black Caps were maniacal in chasing the total down in 12.2 overs.
Southee (7-33 off nine overs) was having trouble with his line early, his second over featuring a wide, a leg bye and a leg-side boundary from Moeen Ali.
But that would prove an anomaly, as he swung New Zealand to victory.
Southee's first three - and four of his first five - wickets saw him cannon into the batsman's off-stump, in a sterling spell.
Southee bowled both openers Ian Bell (eight) and Ali (20), before Gary Ballance (10) miscued a pull attempt to Kane Williamson at cover off the bowling of Trent Boult (1-32).
Out-of-form captain Morgan survived some early nerves, and managed his highest total (17) since his century at the start of the tri-series in Australia in January.
But his wicket, which ended a 47-run partnership between himself and Root, sparked a collapse of 7-19.
An Adam Milne diving catch at long on off the bowling of Daniel Vettori ended Morgan's 41-ball knock.
And it also saw captain McCullum throw the ball straight back to Southee, who picked up five wickets in his next four overs.
Southee rocked the off-stump of both James Taylor (0) and Chris Woakes (one), while Jos Buttler (three) edged through to wicketkeeper Luke Ronchi.
Stuart Broad (four) fended one to mid off where Vettori took a simple catch, before Southee's seventh was Steven Finn (0) - who edged through to Ross Taylor at first slip.
Milne (1-25) finished the innings off when Root skied one to Vettori.
The chase was notable for McCullum's power hitting, as he and partner Guptill (22) became the second NZ pair to combine for 2000 ODI runs, after Stephen Fleming and Nathan Astle.
McCullum's free-wheeling saw him hit eight fours and seven sixes, as he gave New Zealand's net run-rate a considerable boost and helped himself to the equal third-fastest ODI half-century.
The only thing that stopped New Zealand wrapping up victory quicker was the lunch break, the umpires calling for a halt to play with the hosts requiring 12 runs off 41 overs.
Chris Woakes (2-8) bowled Guptill having also ousted McCullum, but it was mere consolation as New Zealand coasted to their third straight win in Pool A.
