The Kiwis were handicapped by having Tomasi Cama sent off in the second minute for punching Rhodri McAtee before skipper DJ Forbes was sent to the sin bin. The Welsh made their superior numbers count but the underdogs fully deserved their victory.
The Kiwis opened the scoring through Nafi Tuitavake but McAtee responded with two touchdowns before the Welsh cut loose to score further tries by Aled Brew, Tal Selley and Rhys Webb swept the rampant Welsh to a 28-5 lead.
New Zealand reduced the lead with a try by Viliame Waqaseduadua but by then it was too little too late.
Wales followed their shock victory with a 24-15 defeat to Australia in their second pool game but guaranteed a quarter-final slot against Kenya when beating minnows Niue 34-10 who had nearly pulled off a shock themselves when restricting the Aussies to a narrow 22-17 victory.
Fiji also suffered a major shock on the opening day with a defeat to the fast-improving USA.
The Americans recorded two victories in the day to confirm their place in a second successive Series Cup quarter final.