Azam scored a 44-ball 69 while Zaman made a 33-ball 43 for Pakistan after they were sent in to bat at Gaddafi Stadium.
Azam saw his opening partner Saim Ayub fall in the second over for just one but that did not deter him as he added 73 for the second wicket with Usman Khan who made a brisk 24-ball 31.
Azam hit six boundaries and two sixes in his 34th T20I half-century before he was bowled by pacer Ben Sears in the 15th over.
Zaman hit four boundaries and a six before he was smartly caught by Mark Chapman on the boundary off Zak Foulkes as Pakistan managed 55 in the last five overs.
Shadab Khan hit a six and a four in his five-ball 15 not out.
New Zealand made three changes as they brought back Tim Seifert, Cole McConchie and Foulkes while pace spearhead Shaheen Shah Afridi returned for the home team.
New Zealand won the third and fourth matches while Pakistan took the second after the first in the series was abandoned.
