Abdul Razzaq, who hit a superb 34-run cameo, then took figures of three for 13 and
skipper Shahid Afridi picked up four for 14 as Pakistan bowled out their opponents for just 80 to record their biggest victory in T20 cricket.
New Zealand were never in with a shout of getting the required runs, with their top four batsmen all dismissed for ducks.
After winning the toss, dismissed Shehzad and Mohammad Hafeez (34) shared an explosive 81-run opening stand that was finally broken by James Franklin, with Hafeez caught at extra cover.
Shehzad brought up his maiden T20 fifty in 41 deliveries, but was trapped lbw in the 11th over by Franklin when going for consecutive boundaries.
New Zealand managed to stem the flow of runs in the middle overs, and also picked up the wickets of Younis Khan (five), run out by Nathan McCullum, and Asad Shafiq (eight), caught at long-off.
But with Afridi out for just 14, Umar Akmal provided stiff resistance in the final overs with his 30, while Razzaq smashed three boundaries and three sixes in the final two overs for his unbeaten 11-ball innings.
In sharp contrast, the hosts lost their top five batsmen with just 11 runs on the board.
Martin Guptil, Jesse Ryder, Dean Brownlie and Ross Taylor departed in the space of just 13 deliveries without troubling the scorers, with Razzaq and debutant Tanvir Ahmed doing the damage around Brownlie's run out.
Following Razzaq's third scalp - Franklin bowled for three - Scott Styris led the fight back with some quick boundaries, but spinner Abdur Rehman bowled Peter McGlashan to leave the Black Caps reeling at 36 for six.
Afridi got rid of McCullum, trapped lbw for eight, before clean bowling both danger-man Styris for 45 and Tim Southee (nought) in successive deliveries.
And the Pakistan captain wrapped up proceedings in the same fashion, bowling Kyle Mills for seven, as victory came with just over four overs remaining.
