Wicketkeeper-batsman Hay reignited New Zealand after a lull midway through their innings, smashing 22 runs in the final over bowled by Mohammad Wasim with two sixes and two fours to finish on 99 not out off 78 balls.
It was the 24-year-old's highest score and his pyrotechnics late on guided New Zealand to 8-292, with Muhammad Abbas scoring 41, after the top-order batsmen all got good starts but failed to make significant scores.
Pakistan then struggled in windy, overcast conditions in their reply and lost 5-32 as pace bowlers Sears (5-59), Jacob Duffy (3-35) and Will O'Rourke (1-19) extracted plenty of bounce from the wicket.
Haris Rauf walked off following a concussion check after he was hit on the helmet by O'Rourke with Pakistan seven down, but his replacement Naseem Shah frustrated the hosts by scoring 51 in the company of Faheem Ashraf, who made 73.
New Zealand delivered the final blow through the impressive Sears, who had Naseem caught behind as Pakistan finished on 208 in 41.2 overs.
Champions Trophy runners-up New Zealand won the opening ODI in Napier by 73 runs last Saturday thanks to Mark Chapman's 132 and Nathan Smith's 4-60. The Black Caps also secured the preceding Twenty20 International series 4-1.
The final ODI will be played in Mount Maunganui on Saturday.
