Oram's dismissal, when England took the new ball in fading light, left New Zealand struggling at 242 for six, needing a further 196 runs on the final day to save the Test.
Only one further delivery was allowed before the umpires called the players in four overs early, leaving McCullum on 43 not out with Daniel Vettori, the last recognised New Zealand batsman, yet to score.
Vettori appeared dismayed that New Zealand were not offered the light when England took the new ball, given that the players had earlier been off the field for eight minutes when it was deemed too dark.
Set a world record fourth innings target of 438 to win, New Zealand struggled to 173 for five before Oram and McCullum began putting the innings back on track.
However, when Ryan Sidebottom broke their 69-run partnership, with Oram caught by Kevin Pietersen at second gully, he put England back on course to level the series.
Although it could also be said New Zealand only progressed as far as they have thanks to below par fielding by England in which eight catches have been grounded so far.
The tourists resumed the day in cold blustery conditions on 277 for nine and added a further 16 runs before the innings ended with Monty Panesar caught by Ross Taylor at slip off Chris Martin for 10, leaving James Anderson 12 not out.
Anderson's fitness had been in question when he left the ground on crutches Saturday evening after twisting his ankle during a warm-down game of football.
A statement was issued saying a decision on his fitness would be made shortly before play began on Sunday.
However, the fast bowler who was the chief destroyer in New Zealand's first innings of 198, taking five for 73, showed no lasting discomfort and bowled impressively through the New Zealand second innings to have 1-54.
New Zealand reached 18 before Jamie How was the first to go, caught in close by Ian Bell off Sidebottom for eight.
Matthew Bell, who never looked comfortable, was dropped by Paul Collingwood on 27 but added only two more runs before Tim Ambrose completed the job off the bowling of Stewart Broad.
Five balls later Broad claimed the prized scalp of New Zealand's senior batsman Stephen Fleming who shouldered arms to a ball which nipped back and clipped his off stump for 31. Fleming received a standing ovation as he left his home ground for the last time as a Test player.
Matthew Sinclair and Taylor put on 81 for the fourth wicket, which ended with Anderson's first delivery after tea when Sinclair pushed a wide delivery straight to Ian Bell at cover.
Taylor went on to score 55, following his first innings 53, to become the first New Zealand batsman in four years to post half centuries in both innings of a Test.
His stand came to an end when he was trapped in front by Sidebottom who ended the day with 3-72, while Broad has 2-38.
New Zealand won the first Test in Hamilton by 189 runs with the third and final Test due to start in Napier next Saturday.