Still England kept battling, and five minutes from time it seemed they might have won it. Courtney Lawes charged down TJ Perenara's box-kick, Underhill collected and raced away, dummying Barrett on his way to the line.
But the All Blacks fought back by scoring 16 unanswered points with full-back Damian McKenzie's 39th-minute try supplemented by Beauden Barrett's conversion, and two penalties either side of a drop-goal - the fly-half's first in 71 Test matches.
Beauden Barrett's dropped goal and penalty put the All Blacks ahead on the hour mark, setting up a dramatic finale.
"I thought we played the final 20 exceptionally well, we'll take enormous confidence from that".
Jones, who coached Japan from 2012 to 2015 and masterminded their famous win over South Africa in the last World Cup, has been playing close attention to how they are developing under Jamie Joseph. You benchmark yourself against New Zealand.
He believes opponents are often bewitched by New Zealand's dazzling skills, reducing them to the role of spectators as their try-line is repeatedly breached before coming to their senses.
"Naturally you feel as though you have to play a lot of rugby to get back in the game and narrow the margin - and we did that".
"We're obviously devastated", Jones said.
But Hansen says the famous All Blacks will be wearing their poppies with pride.
The build up to the match was very different to how it would have been two years ago, when there was talk of England changing their autumn internationals to accommodate a match against the All Blacks following the whitewash win in Australia.
"At that stage of the game, they could be playing the Spice Girls and I wouldn't know what's being played", Jones said.
"It's a great opportunity to assess where our game is at and we're really looking forward to it".
"If the referee shouts ball is out then he's offside".
Opposite number Steve Hansen insisted that Lawes was a mile offside, with his only fear that the officials would not be "brave enough" to overturn it. "We're going to be absolutely ruthless".
As Jones picked through the bones of England's one-point defeat to the All Blacks, he was asked what advice he would give Japan ahead of Saturday's match. "We have got to fix things that didn't work today and if we do that we are on the way to being the best in the world which we always set out to be".
The co-captaincy arrangement with Owen Farrell is a novelty which those outside the England camp are labouring to accept and understand. "You look at it, they have been together for three months, we've been together for less than three weeks". Goodhue was unavailable for selection in Yokohama due to illness but has recovered in time to be considered for the Test with England.
"We've got natural athletes who want to run and carry the ball and pass the ball and have terrific instincts and want to play what's in front of them", he said.