Reigning world champions England, meanwhile, are a distant 13/1 shot, which represents an accurate assessment of the current gulf in standards between two countries whose rugby rivalry began 101 years ago.
New Zealand though, were red-hot favourites on their last Twickenham visit a year ago, only to escape as relieved 23-19 victors after tries in each half from Tana Umaga and Keven Mealamu.
The most abiding memory of that match was provided by New Zealand's temporary reduction to 13 men when they had two players sin-binned - and England's subsequent failure to make their numerical advantage count.
Bath lock Grewcock, who wins his 65th cap on Sunday as comfortably the most experienced member of an injury-hit England side, knows they cannot allow any repeat chance to slip.
"We have to learn the lesson from last year where we lost the game when New Zealand had a couple of guys in the sin-bin and we still didn't capitalise," he said.
"The big thing for us is that if we get these opportunities, then we have to make sure we get the points.
"There are not too many weaknesses in this New Zealand team, and we are obviously looking at the videos trying to find any small areas we can exploit."
Grewcock will be joined by five Leicester forwards in an England pack that must dominate their opposite numbers to have any chance of tearing up world rugby's form-book.
England are reeling from five successive defeats - their worst results sequence since the early 1970s - which has piled pressure on head coach Andy Robinson going into an autumn series of Tests against New Zealand, Argentina and South Africa (twice).
Robinson's degree of difficulty for a game that will mark Twickenham's new South Stand opening, increasing capacity to 82,000, has been compounded by an alarming injury toll.
A dozen candidates for Sunday's encounter have been sidelined, while Robinson fields three new caps in the back division - Wasps wing Paul Sackey, Gloucester centre Anthony Allen and Bristol scrum-half Shaun Perry.
But England attack coach Brian Ashton insists there is cause for optimism ahead of an encounter the All Blacks are widely expected to win comfortably.
Ashton said: "All the players are very positive, and they have the belief which is essential when you are up against as good a side as New Zealand.
"I was encouraged by the number of line breaks we made on the summer tour in the first Test against Australia, but we must capitalise on them more, as and when they come on Sunday.
"I've been working with the players and helping them change their mindset for this game, and we are working with a stronger squad than we had in the summer because a number of players who weren't available for that tour are now.
"There are positive signs the players are communicating better, and I am happy with that."
England, meanwhile, successfully avoided any further disruption when Leicester lock Ben Kay's fitness was confirmed to face the All Blacks.
Kay suffered a leg injury during Tigers' Heineken Cup victory over Cardiff Blues last weekend, which restricted his training during the early part of this week, but he will take his place as planned alongside second-row partner Danny Grewcock.
Captain Martin Corry, who leads his country for the 11th time on Sunday, backs Grewcock's call for a more clinical approach.
"People ask whether we need major or minor surgery to get back on track," said Corry.
"I feel we've been guilty of creating a lot of chances without the scoreboard reflecting the fact. I see getting the execution of those chances as important surgery."