Ian Bell had made a fluent 73, but his dismissal – and that of Kevin Pietersen two overs later – left England 149 for four, requiring a further 80 off 84 deliveries.
That was whittled down by Collingwood and Owais Shah, before the captain hurried England home with a thrilling display of hitting that saw him take 28 off nine balls.
Though their target could have been significantly lower – New Zealand recovered from a perilous 64 for five, and then 95 for six – England can take heart from a bowling and fielding display that was as far removed from their previous performance as one could wish to see.
Stuart Broad emerged as England’s best bowler – his figures of 3-32 included a final over costing 15 – while Collingwood claimed 3-43 and James Anderson 2-41.
But Jacob Oram’s superb 88, allied to a rapid 42 from Daniel Vettori, enable New Zealand to post a respectable total on an even-paced pitch at Eden Park.
England saw Brendon McCullum and Jesse Ryder share a record opening stand for New Zealand in Hamilton, but they were separated within two overs here the former caught at second slip via his glove as he tried to lean back out of the way of an Anderson bouncer that followed him.
Jamie How, frustrated by a lack of scoring opportunities, sliced a drive off Broad to backward point, where Collingwood took a smart catch on the move low to his left.
Ryder fell for 23 three balls later, caught at deep square-leg as he attempted to repeat the pick-up six off Anderson from earlier in his innings, and England’s grip was strengthened when Scott Styris pulled Broad firmly to a stretching Dimitri Mascarenhas at midwicket.
Ross Taylor and Peter Fulton spent seven overs adding 11 before Fulton played around a straight delivery from Collingwood; when Oram inside-edged Ryan Sidebottom for four, it represented New Zealand’s first boundary for 60 balls.
Oram overcame a scratchy start to loft Mascarenhas imperiously over long-on – one of four sixes in his innings – but he had another maximum chalked off when umpire Asad Rauf called dead ball; he was not in position behind the stumps when Collingwood ran in to bowl.
It was the first of two strange incidents in the 30th over, the second of which saw Taylor depart for 31. He was struck on the pad playing forward, and Rauf set off towards the off side – as if to signal an unsuccessful appeal – before stopping to raise his finger.
Captain Vettori batted with considerable intelligence, mixing driven singles down the ground with the occasional leg-side heave as he dominated a stand of 74 – a New Zealand record for the seventh wicket against England – in just 12 overs with Oram.
However, one such shot brought about his downfall, a pull off Collingwood finding only Shah at deep square-leg.
Kyle Mills accompanied Oram for the addition of 30 runs before being hurried into a pull stroke, but Paul Hitchcock’s presence allowed Oram to open his shoulders late on.
Broad was despatched for two sixes in his last over – the only boundaries he conceded – and it took a splendid catch by Bell, diving over his shoulder at midwicket, to bring Oram’s 91-ball innings to an end.
Phil Mustard managed one top-edged six over the wicketkeeper’s head before he became a seventh run-out victim of the series – Vettori hitting at the non-striker’s end from mid-off – and mounting pressure prompted Alastair Cook to swat Oram to mid-on after the rain break.
Bell batted with supreme confidence en route to a 53-ball fifty containing nine boundaries, and Pietersen struck Paul Hitchcock for three successive fours to suggest he was finally finding his best touch.
But both perished in quick succession, Bell leg before to Vettori’s quicker ball despite getting an inside edge, and Pietersen trapped in front aiming across the line.
That Shah contributed just 18 to an unbroken stand of 80 for the fifth wicket reflected the brilliant manner in which Collingwood orchestrated the final stages of the run-chase.
The intensity in his eyes as he stomped from the pitch not only spoke volumes for the importance he placed on this result, but also suggested his appetite will be far from sated by one morale-boosting victory.
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