It was far from a vintage performance by the reigning world champions, who were guilty of uncharacteristic handling errors and sometimes poor decision-making.
New Zealand scored four first-half tries, wing Julian Savea crossing twice and his fellow wing Waisake Naholo - back in action 10 weeks after breaking his leg - also touching down, while hooker Dane Coles went over wide out.
But they were restricted to only three second-half scores, with number eight Kieran Read adding a 48th-minute try and Savea completing his hat-trick before substitute Malakai Fekitoa crossed.
The biggest cheers among a 69,000 crowd were reserved for Georgia, whose full-back Beka Tsiklauri claimed an early breakaway try, with fly-half Lasha Malaghuradze outshining his celebrated opposite number Dan Carter in the goalkicking department.
While an out-of-sorts Carter missed three conversions out of seven, Malaguradze added the extras to Tsiklauri's try and landed a long-range penalty.
"You are trying to qualify for a quarter-final, and you are trying to do things with a purpose. You are trying to work on certain parts of your game," Hansen said.
"There were a lot of things we could have done better, for sure.
"Our skill-execution at times was not great, but if we had one problem that I would think would be the easiest to fix in this team, it would be skill-execution. We have plenty of talent.
"You don't get any gold medals for winning these games, you just get to qualify. We are in the quarter-finals, which is quite exciting.
"We've had little bits of problem-solving in the tournament that we needed to do. It's nice to be put under that pressure.
"It would be great if we were winning by more points, but it doesn't do anything for us. What we are getting at the moment is great. It's making us have to go away and think about our game and work on various parts of it and getting it better."
All Blacks skipper Richie McCaw, meanwhile, dismissed any injury fears after he made a 60th-minute exit when he was on the receiving end of a crunching tackle and immediately had ice applied to two separate areas on his leg.
"I just got a couple of bruises on my shin and quad (thigh). I could have carried on. A couple of days rest, and I will be fine," he said.
"I thought from a physical point of view, the Georgians have shown in the first couple of games, they are big boys. Tonight was pretty physical.
"For a lot of the game, especially up-front and defensively, we took a step up. If we look at the game as a whole, some of our errors were disappointing, but that is an easy thing to fix.
"It wasn't perfect out there, but I thought some of our intensity was a definite step up."
Georgia remain on course to secure third place in the group and automatic qualification for the 2019 World Cup in Japan, and their head coach Milton Haig was delighted with the display.
"I am a proud coach," he said. "I asked the boys during the week to show a bit of pride and show the rugby world what Georgian rugby is all about, and for large parts of the game tonight that's what we did.
"It was pretty plain to see that defensively we put some pressure on the All Blacks, and that is not an easy thing to do. When we got our timing right, we made some pretty good tackles."
Haig, meanwhile, repeated his belief that if Georgia could be added to the current Six Nations mix it would benefit world rugby.
"That is certainly something that publicly I have been speaking about," he added.
"Something like that for our development is absolutely crucial for us. If we are to develop, it is the kind of competition we need to be in. I think it would grow the game globally, and open up another big market in eastern Europe."