The hosts led 16-15 going into the final 16 minutes, but the All Blacks were irresistible from thereon in and piled on 19 unanswered points in a spell of awe-inspiring dominance.
Beauden Barrett's superb chip-and-chase try nine minutes from time proved pivotal as the New Zealand marked Richie McCaw's 100th game as captain with an entertaining win to finish their tour in style.
Until that moment of ingenuity the hosts had their noses in front, but Barrett's brilliance dashed Wales' hopes of making history on Saturday, with Kieran Read crossing the whitewash soon after and Barrett doubling his try tally in the closing stages.
The hosts played their part in an enthralling showdown, set against the backdrop of a passionate and noisy home crowd in Cardiff, but New Zealand - showing 12 changes from the second-string team that beat Scotland last weekend - proved too strong.
Leigh Halfpenny's early penalty handed Wales the advantage, but Barrett's three-point effort, struck from a far more testing distance, levelled matters in the 24th minute.
A presentable try-scoring opportunity passed Wales by on the half-hour mark when Sam Warburton found a gap in the visiting defence, but his pass for Alex Cuthbert on the overlap was forward.
Poor handling from Sonny Bill Williams thwarted the visitors at the other end as a compelling first half drew to a close with New Zealand applying pressure in the 22.
That was how they started the second half, too, and the All Blacks got their reward in the 43rd minute as International Rugby Board (IRB) World Player of the Year nominee Julian Savea was the beneficiary of some poor game management from Halfpenny.
The full-back launched an ill-advised attempt to run the ball out of danger and was halted in his tracks by Read, with the turnover ball quickly recycled and Savea on hand to touch down after being picked out by Conrad Smith.
Wales' response was almost immediate and Rhys Webb took the leading role, exchanging passes with Toby Faletau to leave the New Zealand defence chasing shadows.
With both efforts converted, the scores were tied at 10 apiece, but neither side seemed content with that state of affairs.
Halfpenny's nerveless long-range three-pointer put Wales ahead in the 52nd minute, while heroic defending denied McCaw a try on his landmark appearance, only for a quick switch of play to allow Jerome Kaino to touch down.
A missed conversion left the deficit at just two points and that was eclipsed by Halfpenny's reliable right boot 13 minutes from time, but Barrett's neat chip - aided by a favourable bounce - led to the away side chalking up another seven points.
Victory was assured in the 73rd minute when Read charged down Mike Phillips' attempted clearance and raced away to touch down in the corner, with Barrett adding the gloss and extending Wales' long winless run against New Zealand.