Zimbabwe captain Craig Ervine, who won the toss, wanted his top-order batters to put runs on the board but instead the home team were dismissed inside two-and-a-half sessions on the opening day for their second-lowest innings total this year.
New Zealand were 0-92 when stumps were drawn in Bulawayo, with Devon Conway unbeaten on 51 after completing his 12th Test half century and Will Young also looking solid on 41 not out.
The return of Brian Bennett, Ben Curran and Sikandar Raza in the longer format of the game did not help against the incisive bowling of Henry as he consistently challenged the batters with his intriguing line and lengths.
New Zealand's sharp fielding saw them lifting the tri-series trophy last week in Harare when Henry bowled a terrific last over and gave away only three runs with South Africa in sight of victory.
But on Wednesday New Zealand missed two catching opportunities when top scorer Ervine (39) and Tafadzwa Tsiga (30) both got dropped early in their innings.Â
Despite getting second chances, both batters struggled during the 54-run partnership against the immaculate Henry and Nathan Smith (3-20), with third seamer Will O'Rourke also going for just two runs an over in his 13 overs.
Mitchell Santner, captaining the Black Caps for the first time in the absence of injured Tom Latham, hoped his three fast bowlers would get the most out of a soft pitch after he lost the toss and was asked to field first.
And Henry didn't disappoint.
He got the outside edges of Bennett (6) and Curran (13) during his impressive opening spell of seven overs. He then found the outside edge of Nick Welch (27) at the stroke of lunch to leave Zimbabwe rocking at 4-67.
Smith had reduced Zimbabwe to 3-31 when in-form Sean Williams (2) chopped a short ball back onto his stumps.
Raza lasted for only two runs in his return to the longer format as he fell soon after lunch when he tried to fend Henry's sharp short ball and lobbed an easy catch to wicketkeeper Tom Blundell.
Henry polished off the tail quickly as Santner pounced on a diving catch and held on to a leading edge of Blessing Muzarabbani after Newman Nyamhuri had been caught by Young.
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