After quickly losing Zak Crawley in their reply, England recovered impressively as Ollie Pope (51 not out) and Alex Lees (34 not out) led them to 90-1 at the close.
It was Mitchell’s day as the journeyman with little Test pedigree, until this series, continued to seize his chance.
Six years ago, Mitchell had a season playing for Blackpool in the Northern Premier League and scored just two centuries.
The 31-year-old batsman arrived in England with just one Test hundred to his name since his 2019 debut, but now he has three following his 108 at Lord’s.
Mitchell’s latest century came in 318 balls, including 23 fours and four sixes, with England dropping him for the second time in the match just after he reached his ton.
“It was very rewarding to get the individual achievement but also to help the boys out,” Mitchell said.
“It’s cool to get some scores. That is the wonder of Test cricket, when you get a few chances you have to make the most of it.”
New Zealand showed why they are the Test world champions, ruthlessly pressing home their advantage after scoring 318-4 on Friday.
“It was good to see the guys having a good time out there and scoring runs after a couple of tough days. We hope for a big first innings score,” England batting coach Marcus Trescothick said.
Mitchell, who scored 81 on Friday after being dropped by Joe Root on three, moved within touching distance of his ton after pulling a short James Anderson delivery for a crunching four.
He brought up his century with a fortuitous edge off Matthew Potts.
If that was an ungainly way to reach the hundred, it was out of character with the rest of Mitchell’s classy innings.
As he did on Friday, Mitchell went on the offensive against spinner Jack Leach but, on 104, he rode his luck with a lofty blow that was dropped by Potts as it trickled to the boundary.
Blundell nudged a single off Leach to reach his third Test century from 191 balls, but he was dismissed when he drove Leach to Stokes at mid-off.
Bracewell showed no signs of stage fright as he repeatedly battered Potts to the boundary before rain provided a merciful break for England.
When play resumed, Anderson induced an edge from Bracewell and Root made the catch, ending the 91-run sixth wicket partnership.
That exposed the New Zealand tail and Stuart Broad dismissed Kyle Jamieson (14) and Tim Southee (4) in the same over.
Trent Boult added some lusty blows in a pesky last-wicket stand of 33 before Mitchell was caught behind off Potts.
New Zealand’s mammoth total was their highest ever score in England, beating their 551-9 declared in 1973.
After watching New Zealand bat for nearly two days, Crawley lasted just six balls.
Boult produced a beautiful piece of seam bowling that left Crawley in two minds as it clipped the edge and was caught behind by Blundell to leave England 6-1.
The fielding woes that tormented England haunted New Zealand as well when Lees, on 12, was dropped in the slips by Mitchell off Southee.
Pope settled England’s nerves with an assault on Matt Henry that included two sumptuous fours and a top-edged six.
Mitchell had benefitted from England’s drops, but he was returning the favour, putting down Pope on 37 from an edge off Boult.