Opener Ahmed Shehzad smashed a brilliant 113 while stand-in skipper Shahid Afridi knocked a blistering 26-ball 55 to lift Pakistan to 364-7 in 50 overs — their highest one-day total against New Zealand.
New Zealand were bowled out for 217 in 38.2 overs with Kane Williamson top-scoring with 46 while Luke Ronchi made 41.
Left-arm spinner Haris Sohail grabbed 3-45.
Pakistan won the first match in Dubai by three wickets while New Zealand clinched the second in Sharjah by four.
The fourth and fifth matches will be played in Abu Dhabi on Wednesday and Friday.