Carter stretched New Zealand's lead to 18-9 when Wales went off their feet at a ruck, before the fly-half cut loose to claim his side's third try.
The Crusaders star exchanged passes in midfield with Jane to create a half-gap that he jinked through, cutting right to beat Andrew Bishop to the line and Carter then converted his own try.
New Zealand coach Graham Henry had bolstered his front row at half-time by sending on Tony Woodcock for Ben Franks at loose-head, and the Wales scrum started to creak noticeably from then on.
In the loose Wales were still doing heroically, Gavin Thomas impressing on his first Test outing since 2007 and giving able support to Jonathan Thomas and skipper Jones.
A New Zealand ruck on the Wales line was turned over and the ball kicked upfield.
Halfpenny hacked on and the Cardiff Blues flyer and fellow wing Prydie bore down on the New Zealand 22, only for replacement Kahui to show excellent pace to outstrip the Welsh pair.
Any faint hopes of a fight-back were soon extinguished by Carter, who kicked a third penalty and then scored a sublime second try.
New Zealand spun the ball wide and Carter went 50 metres, past Prydie, Bishop and Byrne, to score a brilliant solo try he then converted himself.
As Wales tired Kahui again showed his pace to break through for a fifth New Zealand try, underlining a second-half dominance that swept Wales aside.
With the second Test to come in Hamilton next week, Wales coach Warren Gatland must help his players absorb another harsh lesson at the hands of a Tri-Nations side - that mistakes are punished ruthlessly and clinically.
2010 Event for Wales and New Zealand:
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When: Saturday 7th November 2009 - 5:15pm
Where: Millennium Stadium, Cardiff City Centre
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