Guptill struck 13 fours and two sixes but the next highest score was Ross Taylor???s 11, as the home side collapsed to 157-7 in 30.1 overs after winning the toss.
Seamers Elton Chigumbura (2-21) and Tinashe Panyangara (2-28) jolted the New Zealand batting, with wickets falling at regular intervals at Bert Sutcliffe Oval before heavy rain washed out the match.
New Zealand struggled from the off as Brendon McCullum (eight) fell to the fifth ball of the match and Kane Williamson (six) departed soon after, before Guptill led something of a recovery by adding 43 with Taylor.
But wickets continued to tumble and Guptill was seventh to go, dismissed by part-timer Sikander Raza just before rain brought the game to an end.
New Zealand open their World Cup campaign in Group A with a game against Sri Lanka at Christchurch on February 13, while Zimbabwe meet South Africa in Group B match at Hamilton a day later.