New Zealand scored seven tries on Saturday, including two each for wings Caleb Clarke and Sevu Reece. Fullback Ruben Love, prop Tamaiti Williams and centre Rieko Ioane also went over as they finished their Autumn International series with three wins from four games.
Wales scored a late try through wing Louis Rees-Zammit to record the most points they have ever managed in Cardiff against the All Blacks, beating the previous mark of 25.
Japan's win over Georgia on Saturday means Wales are guaranteed 11th spot in the world rankings when the  2027 Rugby World Cup draw is made on December 3, no matter what happens when they face the Springboks next weekend.
The hosts did not help themselves with yellow cards for prop Gareth Thomas and No.8 Taine Plumtree that left them a player light for 20 minutes in the second half.
But coach Steve Tandy will be pleased with how they competed for large parts of the match.
The scoring was tit-for-tat until the visitors led 24-21 in the 50th minute before New Zealand streaked ahead on the scoreboard.
Rogers was the first player to score a hat-trick against the All Blacks since South Africa's Marius Joubert in 2004, and the ability of the home side to open up the visitors in wide areas will be pleasing, as shown again by Rees-Zammit's late score.
New Zealand, however, claimed a 34th consecutive win over Wales, despite resting several regulars.
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