Following their chaotic 115-run defeat at Lord's in the opening Test, New Zealand, having been put in on Wednesday, were wobbling on 4-107 before Tom Blundell and Glenn Phillips gave them a foothold in a game they can't afford to lose.
Blundell made 51 as he shared an 81-run fifth-wicket partnership with Daryl Mitchell and then a sixth-wicket stand of 75 with Phillips, who was 49 not out at the close having survived a fierce spell from Jofra Archer, although New Zealand are some way short of an imposing total on a good pitch.
Baker, one of three debutants in an England side showing five changes from Lord's, seized his chance in style while fellow quick Matthew Fisher marked his return, four years after his only other Test, with a wicket.
The build-up to the second of the three-match series was dominated by England captain Ben Stokes and bowler Gus Atkinson being left out amid an investigation into a nightclub incident.
England's record Test run-scorer Joe Root, back as captain for a record-extending 65th time having stepped down in 2022, won the toss on an overcast morning and put New Zealand in on a wicket offering early movement.
Fisher broke through with the last ball of the sixth over as Devon Conway tickled an attempted pull shot down the leg side to debutant wicketkeeper James Rew.
New Zealand captain and opener Tom Latham fell shortly before lunch, getting a leading edge to a ball by Archer with Jacob Bethell pouching a sharp rising catch.
Having reached 2-75 at lunch, New Zealand added only four runs after the interval before Henry Nicholls chopped a rising delivery from Josh Tongue on to his stumps for 24.
Rachin Ravindra also got a start, playing positively, but having struck six boundaries to reach 33 he became Baker's first Test victim, edging to Bethell at gully.
Just as the pressure was mounting on England, Mitchell fell for 44, pulling straight to Emilio Gay at short mid-wicket to give Baker his second wicket.
Blundell reached his half-century with a four off part-time spinner Bethell, but his rash dismissal two balls later, having the ball straight to Root at midwicket, summed up New Zealand's day.
Archer produced a ferocious late burst of short-pitched bowling to have Phillips ducking and diving but it was a Bethell full toss that gave England a bonus seventh wicket as Nathan Smith ballooned a catch to Jordan Cox.
