The All Blacks twice led by 14 points, having caught England cold with two converted tries in the opening eight minutes through flanker Dalton Papali'i and hooker Codie Taylor.
Rieko Ioane's superb try early in the second half made it 22-6 before Beauden Barrett added a drop-goal to put New Zealand a seemingly impregnable 19 points ahead.
England, however, hit back with three tries in the closing nine minutes, Stuart twice powering over either side of a try by full-back Freddie Steward.
Marcus Smith's conversions of those last two England scores helped seal only the second draw in 43 meetings between the two sides following a 26-26 all encounter at Twickenham in 1997.
This was the first meeting between the teams since England's 19-7 win in a 2019 World Cup semi-final in Japan that ended the All Blacks' eight-year reign as world champions.
All Blacks coach Ian Foster had picked his strongest squad, with the team resembling the side that thrashed Wales 55-23 in Cardiff a fortnight ago rather than the one that edged out Scotland 31-23 at Murrayfield last weekend.
England captain Owen Farrell and New Zealand lock Brodie Retallick were both winning a 100th cap for their respective countries.
A capacity Twickenham crowd of over 80,000 heeded England forwards coach Richard Cockerill to "drown out" the All Blacks traditional pre-match haka or ritual challenge, with home fans belting out 'Swing Low, Sweet Chariot', England's unofficial anthem.
But an unconcerned New Zealand took just three minutes to open the scoring, with flanker Papali'i reading the play well to intercept a pass from novice England scrum-half Jack van Poortvliet before sprinting in unopposed from 45 metres for a try between the posts.
Jordie Barrett, back in midfield, converted and the All Blacks, who'd won 33 of their previous 42 Tests against England with one draw, were 7-0 up.
Barnstorming start
In Yokohama three years ago, it was England who had made the barnstorming start, but four minutes after breaking the deadlock on Saturday, New Zealand had their second try.
Retallick, packing down alongside New Zealand captain Sam Whitelock for a record-breaking 64th Test as a second-row duo, won a line-out and Taylor rumbled over for another converted score to make it 14-0.
Ioane touched down in the 17th minute but French referee Mathieu Raynal, after consulting the television match official, disallowed the try for an illegal neck roll challenge by the centre in the build-up.
England's first prolonged spell in the All Blacks' 22 eventually led to a 23rd-minute penalty, with Farrell making no mistake from close range.
New Zealand, however, restored their 14-point lead through Jordie Barrett's penalty on the stroke of half-time.
Fly-half Smith, taking over kicking duties following a knock to Farrell, landed a penalty to leave New Zealand 17-6 ahead.
England laid siege to the All Blacks' line only for superb defence to keep them at bay.
New Zealand then struck in style, with full-back Beauden Barrett's cross-kick gathered by wing Caleb Clarke, whose inside pass released Ioane, with the centre sprinting three-quarters of the length of the field for a try in the left corner.
Jordie Barrett couldn't convert but, with 10 minutes left, full-back Beauden Barrett's drop-goal appeared to have made the gane safe,
Moments later, however, he was sin-binned and England capitalised when Stuart was awarded a try after a lengthy TMO check.
A brilliant counter-attack and some slick passing sent Steward in at the corner before relentless forward pressure from England led to Stewart's second try and Smith's levelling conversion.
