For 60 minutes, England was in the directors' chair courtesy of tries from Chris Ashton and Dylan Hartley, and but for a disallowed try at the end may well have pulled it off.
But part of the All Blacks' magic is poise and patience, and the double world champions hit back to escape with a 16-15 victory under the drizzle of southwest London.
With the World Cup less than a year away it was a significant result for both sides.
For New Zealand, it added to its reputation as one of sport's most dominant winning machines, and was, perhaps, proof that the recent defeat against South Africa was a blip.
For England, shorn of a raft of key players through injury, it was another step in the right direction following last week's win against South Africa in the wake of a disappointing year that has put Australia's Jones on the ropes.
"Sometimes the game loves you, sometimes it doesn't," said Jones, whose side got away with a controversial late decision which could have cost them the win against the Springboks.
"We really stuck it to them. It's a really good step forward because you benchmark yourself against New Zealand."
The All Blacks hadn't been to the home of English rugby for four years, but like the opening chords of a long-awaited Rolling Stones tour, the hair-raising haka told you they were back.
Not that you could hear the warrior's chants, such was the deafening rendition of "Swing low, sweet chariot," English rugby's anthem. The thunderous noise at Twickenham told you this was special.
The match was also billed as a clash of styles. The All Blacks' electric, attacking rugby -- yielding an average of four tries in its last 12 games -- against England's tighter, more forward oriented game.
From the outset, Jones' men were muscular, fired up, and precise. They met the Kiwi rapier with a cutlass and cudgel.
A flowing early move sent winger Ashton -- also back for the first time in four years -- over in the right corner.
As if on cue, the stadium PA pumped out the Stones' "Start Me Up," and it was clear England had picked up the challenge of the haka and run with it.
A second try followed, this time from a ferocious forward surge off a lineout to put co-captain Hartley over.
As England surged to a 15-0 lead it looked as if rugby's axis was in full tilt.
But like a wily hunter stalking its prey, New Zealand remained patient, prodding and probing.
And when opportunity knocked the men in black struck with clinical precision.
Slick handling in a pre-arranged backs move put full back Damian McKenzie under England's posts. Beauden Barrett added the conversion and landed a penalty shortly after to go in at the break 15-10 down but on the up.
The All Blacks' engine was purring again after half time, only for a rare dropped pass to scupper a certain try.
Undeterred, England had a near miss of its own, but despite hammering away near the Kiwi line it couldn't quite find a way through.
As Jones admitted, those are the chances you must take against the All Blacks, because when Barrett slotted a drop-goal and then another penalty on the hour mark, New Zealand were suddenly in front.
The All Blacks are renowned for their ability to snuff out tiring opposition in the last quarter, but England hung on tight at Twickenham.
"New Zealand generally run away from teams in those areas but they couldn't," said Jones.
When flanker Sam Underhill turned Barrett inside out and looked to have scored in the left corner off a charged down kick with five minutes left, the majority of the 80,000 crowd erupted with roars that reverberated down the nearby River Thames.
But the referee opted for a TV review and England lock Courtney Lawes was adjudged marginally offside in charging down the kick.
All Blacks' coach Steve Hansen claimed there was "no doubt" it was offside, but said later he was just worried the officials would be "brave enough" to make such a crucial decision.
"I thought England were very good, but I thought we showed a lot of character to be down 15-0 in a hostile environment, with 79,000 not being Kiwis, and the weather conditions -- it wasn't conducive to being able to play razzle-dazzle rugby -- and the boys stuck with it," said Hansen.
New Zealand captain Kieran Read added: "For us it's about trust and belief. We just had to work things out."
After talking to reporters, Hansen set off to find his old mate Jones for a beer.
They'll have much to discuss over the next 12 months.
"It was a fantastic game of rugby," said Jones.
"I tell you, we're excited about where we're going."
England takes on Japan next week, while New Zealand moves on to face Ireland in Dublin.