Guptill, 28, scored more than half of the tourists' second innings runs on the way to setting Worcestershire a target of 246 in 50 overs.
At 169-2 with 20 overs remaining, the hosts looked the more likely winners.
But Worcestershire lost six wickets for 22 runs to subside to 230 all out.
Opener Guptill was one of the Black Caps' stars in their impressive recent World Cup campaign, scoring a competition record 237 not out in the semi-final against West Indies to help New Zealand reach the final.
However, Tom Latham and Hamish Rutherford are the Test incumbents at the top of the order, leaving New Zealand head coach Mike Hesson with a selection quandary before the first Test against England begins at Lord's on Thursday.
New Zealand opener Martin Guptill improved his prospects of selection for next week's first Test against England with an impressive 150 in the tour win at Worcester.