Buffeted by weeks of off-field controversy in which coach Peter Moores was sacked and the Kevin Pietersen non-selection saga took centre stage, England took the field in bad shape.
A hapless first hour in which Cook, Adam Lyth, Gary Ballance and Ian Bell failed to withstand the New Zealand pace attack potentially set the tone for a summer of struggle with the Ashes series to come.
But Joe Root, Ben Stokes, Jos Buttler and Moeen Ali had other ideas.
The quartet posted half-centuries to lift England to a total of 389, laying the foundation for a recovery which brought about a famous victory in an enthralling match.
New Zealand batted well to reply with 523 but Cook had the bit between his teeth.
The captain occupied the crease all day on Sunday to make 153 not out and combined with Root's 84 and an inspired 101 from Stokes, the quickest ever test century at Lord's, England moved into the ascendancy at 429 for six.
Trent Boult knocked over the last four wickets inside the first hour on the final day but England had made a statement and their bowlers backed it up.
James Anderson and Stuart Broad reduced New Zealand to 12 for three and Stokes made a devastating contribution with the ball by dismissing Kane Williamson and Brendon McCullum with successive deliveries.
Spirited resistance from BJ Watling and Corey Anderson proved temporary and Moeen's superb catch at third man to dismiss Boult sealed a 124-run victory for England.
"Today, the way our guys bowled... we fought incredibly hard on a great cricket wicket," Cook told reporters.
"It's been a real team effort this week. It's been a rocky few weeks so to play with such freedom and passion, the lads are pleased with that."
It was a rocky few weeks indeed.
With speculation swirling that Australian Trevor Bayliss is poised to be appointed coach ahead of his compatriot Jason Gillespie the saga continued on Monday.
But on the field Cook and his team laid down a marker ahead of the Ashes.
With the captain back in the runs, Root a flexible and reliable presence in the middle order and the exciting Stokes established at number six, England have a batting order of substance.
Although the pace bowling attack certainly lacks variety, it has the heart and fire to ask questions of the Australians in what promises to be an intriguing Ashes series.
(Editing by Amlan Chakraborty)
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