Grant Elliott and Luke Ronchi both finished unbeaten on 106 in a 221-run partnership between the pair as the Black Caps amassed a massive 373-5 from their 50 overs.
Mitchell McClenaghan then took 4-31 as the tourists ripped through the Leicestershire line-up, bowling them out for 175 in the 43rd over.
After winning the toss and choosing to bat first at Grace Road, New Zealand got off to a surprisingly poor start, with Brendon McCullum (nine) and Martin Guptill (four) both falling to the impressive Atif Sheikh (3-49).
Ross Taylor (77) impressed in particular ??? smashing four sixes ??? in an 87-run partnership with Kane Williamson (45) to rebuild the innings.
But again the visitors lost wickets in a cluster as the pair, and Mitchell Santner (four), all fell within three overs of each other to reduce New Zealand to 152-5 at the halfway mark of their innings.
But Elliott and Ronchi launched a brutal counter-attack with the bat, with 195 runs coming from the final 20 overs.
Leicestershire were never likely to chase down the 374 runs they needed win, especially after Lewis Hill (11) and Ned Eckersley (four) both fell inside the first 10 overs, reducing the hosts to 29-2.
Angus Robson (67) and Umar Akmal (26) offered some brief resistance, before the latter became McClenaghan???s second victim after having bowled Hill.
McClenaghan added the scalp of Neil Pinner for eight as Leicestershire???s middle-order collapsed, losing five wickets for 43.
After Robson finally fell, Sheikh (22) and Rob Sayer (22no) had a bit of fun, smacking a couple of fours and a six apiece, before McClenaghan wrapped up the innings and win with the final wicket of James Sykes for a duck.