Fly-half Colin Slade was drafted in by coach Graham Henry to replace record points-scorer Carter, who will miss the rest of the World Cup with a groin injury.
On a day when winger Zac Guildford scored four of New Zealand's 12 tries at the Wellington Regional Stadium, Slade started for only the fourth time in his nine Tests with the spotlight firmly on him as the host nation made it four wins from as many starts in the pool campaign.
Guildford scored three of his tries in the first half on his World Cup debut as Slade struggled to judge the difficult conditions and only landed five from nine kicks at goal.
Slade's opening-minute kick was charged down and from the breakdown Canada fly-half Ander Monro kicked a penalty to give his side a 3-0 lead.
But Slade set up Guildford's opening try with a long pass before adding the extras.
Victor Vito, starting a test at openside flanker for the first time in place of All Blacks captain Richie McCaw, added New Zealand's second but Slade's kick was off target.
Slade kicked another penalty before failing to convert tries from Israel Dagg and Guildford.
Guildford scored his second try when Canada winger Conor Trainor failed to control a kick into the in-goal area, then made a try for full-back Mils Muliaina.
A third try for Guildford came after 34 minutes when Sonny Bill Williams burst through and kicked for Muliaina who put in Guildford.
Trainor scored a try just before the break, hitting the backline hard and at pace after a scrum from five metres.
Trainor had his second when a breakdown in the All Blacks' midfield allowed the winger to kick through and touch down, Monro adding the conversion.
New Zealand hit back with a try from scrum-half Jimmy Cowan, created by centre Conrad Smith and converted by Slade.
Jerome Kaino scored his first try in the 51st minute and his second in the 67th, on either side of a try from Williams.
Slade converted Kaino's first before handing the kicking duties to Piri Weepu who kicked four from four.
Guildford added his fourth and Vito his second before the end.
After the game New Zealand captain Andrew Hore faced up to the loss of Carter.
He said, in an interview broadcast on ITV1: "You can't lie about it, he's going to be hard to replace as he's a pretty special player."
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