Cam Roigard, Will Jordan, Mark Tele'a and Beauden Barrett scored the tries as the All Blacks beat Italy for the 18th consecutive time, with fly-half Barrett kicking the rest of the away side's points.
Cane, who was part of New Zealand's last Rugby World Cup-winning team in 2015, closed out his Test career with 104 caps while TJ Perenara also played his final All Blacks match as a second half substitute.
"Two special guys. They've been huge parts of the group. (Cane is) a real warrior, always put his body on the line, always gave his everything in the black jersey," said Jordan.
"We didn't have it all our way... We're treading in the right direction. It was an arm wrestle so it's nice to be on the right side of it."
Tommaso Menoncello dotted down late for Italy, with Paolo Garbisi kicking a six further points in a valiant performance.
Gonzalo Quesada's team had been expected to be heavily beaten by a strong All Blacks line-up but fought hard in front of more than 40,000 fans at a freezing Allianz Stadium.
"We are so proud of our performance. That's what we were talking abut in the week, we wanted to be proud of our team," said Juan Ignacio Brex, Italy's captain in the absence of injured Michele Lamaro.
"This has to be our base for the Six Nations."
Jordan passes Lomu mark
Italy led early on through Garbisi's two penalties but the enthusiastic hosts never managed to create any try-scoring opportunities in the opening period, not even with a man advantage following Scott Barrett's yellow card in the 20th minute.
Instead it was the sloppy away side who dotted down the first try of the evening four minutes later through Roigard, who simply strolled through the centre of Italy's defence for an easily converted score under the posts.
Head coach Scott Robertson fumed in the stands in the 34th minute when Will Jordan went it alone with better options yards from the try line, allowing Brex to clatter into him and then Wallace Sititi to stop what looked like a certain try.
But Jordan made up for his earlier error seconds before the break when after a long period of All Blacks pressure he surged onto Beauden Barrett's pass and exploited a yawning gap to slide home for the second converted try of the night.
That try took Jordan up to 38 in international rugby and past All Blacks icon Jonah Lomu, as well as giving his side a 17-6 half-time lead.
Italy battled hard and were camped in the New Zealand 22 for nearly 10 minutes early in the second half but just couldn't break through, not even after Anton Lienert-Brown collected his team's second yellow card of the night.
Cane was applauded off by the whole stadium when he was replaced by Peter Lakai in the 67th minute and three minutes later Tele'a made absolutely sure of the win by dotting down in the corner from Beauden Barrett's pass.
Menoncello then sent the home fans wild with a lovely try after collecting from Marco Zanon, but Beauden Barrett capped a superb display by running in New Zealand's fourth try of a dominant but unconvincing display.
