Chris Martin, New Zealand fast bowler, took two early wickets, but from then on England were always in control with all-rounder Dmitri Mascarenhas doing damage for the tourists with both bat and ball.
Mascarenhas arrived at the crease when the England batting momentum was slowing towards eight an over after a brisk start, and belted 31 from 14 balls including four successive sixes off spinner Jetan Patel.
Brendon McCullum, New Zealand captain, had inexplicably given Patel the ball, replacing debutant Jesse Ryder who had taken the wicket of Owais Shah and conceded only two runs in his sole over.
Patel had the last word when he caught Mascarenhas off Kyle Mills in the following over but by then the England run-scoring tempo was back around a formidable 10 per over.
Kevin Pietersen top-scored with 43 off 23 balls before being neatly caught by a diving Ross Taylor at cover.
Mascarenhas continues with the ball
New Zealand were tight in the field, conceding just two extras, but only Martin seriously threatened with the ball taking 2 for 34 off his four overs.
Mills finished with 2 for 43 but his wickets came in the closing stages when England were hitting out.
Following his batting exploits, Mascarenhas then tied up the New Zealand batsmen with his medium pace deliveries taking 2 for 19 from four overs, while left-armer Ryan Sidebottom finished with an impressive 3 for 16.
Mascarenhas also contributed to the run-out of New Zealand's second highest scorer Ryder as the home side's top order crumbled to 70 for 6 in the 10th over.
Oram's late fireworks, which saw him smack seven fours and two sixes, merely delayed the inevitable, and the only other batsmen to reach double figures were Ryder, who compiled 22, and Mills with a late 11.
The second Twenty20 game is in Christchurch on Thursday with the first of five one-dayers in Wellington on Saturday.
New Zealand and England play three Tests next month.