Opting to bat after winning the toss at the Westpack Stadium, England were bowled out for a paltry 123 with fast bowler Southee returning figures of 7 for 33, the third best in World Cup history after Glenn McGrath and Andy Bichell.
In reply, New Zealand completed the formality in just 12.2 overs with McCullum blasting his way to a 25-ball 77, the batsman reaching his half-century in just 18 balls to set a new record in the showpiece event.
The opener eclipsed his own World Cup record when he smashed pacer Steven Finn for a six, having made a fifty off 20 balls against Canada in the 2007 edition in the West Indies.
His innings was also the equal third-fastest fifty in all One-day Internationals, behind South Africa's A B de Villiers (16 balls) and Sri Lanka's Sanath Jayasuriya (17 balls).
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McCullum went on the rampage from the first ball and was especially severe on Finn, who was smashed for 49 runs in two overs.
McCullum plundered Finn for 44 runs from his 10 balls, which included two fours and six sixes.
He was finally dismissed by Chris Woakes after playing a sensational knock that came at a staggering strike rate of 308.00. This was McCullum's 29th ODI half century in 243 matches.