The tourists began an entertaining final day on 89-2 and opener Martin Guptill went on to boost his case for Test selection with a fine 150 as they reached 275-9 before declaring and setting their hosts 246 to win.
Worcestershire then reached 119-1, 169-2 and 208-4 but their lower order failed to fire and they lost six wickets for 22 runs to fall short, Mark Craig taking 4-56.
Guptill played the key innings when play resumed, his overnight partner Ross Taylor falling for 29 when he picked out a diving Tom Fell off Shaaiq Choudhry (5-57), who was on the way to the first five-wicket haul of his senior career.
BJ Watling (0) and Luke Ronchi (14) also fell to Choudry but Matt Henry (30) gave Guptill fine support in a stand of 81 for the seventh wicket before he was also dismissed by the spinner.
And the 28-year-old Guptill was ninth man out, his 150 having come from 210 balls, featuring 15 boundaries and three sixes.
Tom Latham and Hamish Rutherford are the incumbent Test openers for New Zealand but one-day maestro Guptill has made a strong case for a first Test cap since 2013.
When Worcestershire batted, the top order laid good foundations for their bid to chase down 246, openers Daryl Mitchell (44) and Richard Oliver (47) putting on 78.
Tom Kohler-Cadmore (55) then came to the crease and shared stands of 41 with Mitchell and 50 with Fell (30).
But it was 191-4 when Kohler-Cadmore was caught behind by Ronchi off Neil Wagner and, although Alex Gidman (31) tried to keep the chase on track, off-spinner Craig and medium-pacer Henry (3-58) scythed through the lower order to win the game for New Zealand.
Ed Barnard was last man out with 3.4 overs left to play and New Zealand will now begin to prepare for the two-Test series against England, which begins at Lord’s on Friday.