Johnson made light work of the Black Caps batting order to record career-best figures of 5-39 as the tourists failed to last an hour in being bowled out for 177.
New Zealand resumed on 143 for six still needing 184 runs for an unlikely victory and needing huge performances from Ross Taylor and Daniel Vettori at the crease.
Taylor started the day on 67 while Vettori was yet to spend time in the middle and they initially showed some fight but their resistance lasted less than half an hour as Johnson struck.
A soaring Andrew Symonds pulled off a one-handed catch at point to spell the end of Vettori's stay after the New Zealand skipper played a loose drive to a wide ball from Johnson.
The left-arm paceman then picked up another wicket in his next over when Taylor edged an angled delivery and diving wicketkeeper Brad Haddin took the catch as a defiant knock of 75 came to an end.
Stuart Clark, who returned figures of 4-43, then made it three wickets in fifteen minutes when he removed Iain O'Brien with a slower ball.
With the end nigh, Tim Southee decided to cut loose and smashed two booming sixes off Clark.
It mattered little, though, as the match came to an early end with Johnson completing his five-wicket haul when he removed Chris Martin's middle stump.
Along with first innings figures of 4-30 and a handy second innings knock of 31, Johnson's effort also secured the man-of-the-match award.