The contest at Eden Park served as the All Blacks' first since their World Cup final triumph against Australia last October.
Former captain Richie McCaw, Keven Mealamu, Tony Woodcock, Dan Carter, Ma'a Nonu and Conrad Smith all ended their international careers following the World Cup.
And for long periods it looked as though McCaw's replacement Kieran Read would suffer defeat in his first game as skipper, with Wales producing a performance in stark contrast to their 27-13 defeat to England last month.
But the All Blacks had too much for Warren Gatland's men in the second half and take a 1-0 lead in the three-Test series ahead of the second meeting in Wellington next weekend.
Aaron Cruden, taking over the number 10 role formerly held by Carter, opened the scoring with a penalty having seen a second-minute effort strike the upright but the visitors responded quickly with the game's first try after eight minutes.
Wales - who saw lock Alun Wyn Jones win his 100th cap - pounced on full-back Ben Smith's failure to catch a high kick, a sweeping passing move from right to left sending Taulupe Faletau over in the corner.
Cruden orchestrated an excellent reply for New Zealand, his kick finding Julian Savea out wide to restore their advantage before Smith atoned for his earlier error.
Smith surged through the Wales defence after claiming a high bomb before firing out to Cruden, who in turn set up wing Waisake Naholo to race clear.
A conversion from Cruden gave New Zealand a 10-point lead but, while many may have expected the floodgates to open, Wales fought back well and were rewarded for some expansive attacking play with a pair of Dan Biggar penalties.
There was more to come from Wales before half-time as Rhys Webb crossed to put them ahead once more following a line break from the hugely impressive Liam Williams.
New Zealand levelled through the boot of Cruden eight minutes into the second half, only for Biggar to put Wales back in front with a three-pointer of his own five minutes later having drifted an earlier attempt to the left.
But Naholo squeezed over for his second from a quickly taken penalty and New Zealand established breathing room as Patrick Tuipulotu sent Read over 12 minutes from time.
TJ Perenara and Faletau had tries disallowed by the TMO at either end before Nathan Harris added late gloss to the scoreline in a battling New Zealand win.