The home side declared at 385 for seven after lunch, leaving the Kiwis needing an unlikely 321 to win from 48 overs to level the series, at almost seven runs per over.
A shower delayed play for about an hour and the Kiwis should little appetite for the chase when they resumed in a match dominated by the bat on a lifeless pitch.
When stumps was called early with 20 overs left, the Kiwis were 104 for two, with Ross Taylor on 36 and Kane Williamson on 32.
Johnson, who announced his retirement from international cricket before the day's play, provided something to cheer about for the sparse final day crowd of just over 3,000 when he claimed the wickets of both Kiwi openers.
He had Tom Latham caught on the fine leg boundary for 15, Josh Hazlewood sliding in to take a fine catch.
Johnson, 34, then surprised Martin Guptill (17) with a rising delivery and he fended a catch to Joe Burns at short leg.
Given a guard of honour by the Kiwis when came out to bat earlier in the day, the left-armer finished with 2-20 from six overs, a vastly improved return on his 1-157 in the first innings.
A draw had looked the most likely result when Australia
resumed the day's play with centurions Steve Smith and Adam Voges at the crease.
But the Kiwis removed both before lunch to briefly revive their hopes of a remarkable comeback win.
Smith was caught behind by BJ Watling from the bowling of Trent Boult (2-77) for 138. The form woes of Mitchell Marsh then continued when he made just one, trapped lbw by Doug Bracewell.
Peter Nevill and Johnson set about steadying the ship, adding 61 in quick time and setting the scene for the declaration.
Johnson was honoured by the New Zealanders when he came out to bat, shaking hands with Kiwi Brendon McCullum on his way to the crease.
He made a breezy 29 before he was caught behind from the bowling of Southee.
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