Conway, unbeaten on 136 overnight, showed remarkable composure amid a batting collapse from the Black Caps, who lost their last seven wickets for the addition of 90 runs, to become just the seventh person to record a double ton on his Test bow.
While Wood’s three-wicket burst led England’s fightback on Thursday morning, Robinson finished with four for 75 and was only denied a five-for and a place on the honours board after Stuart Broad shelled a relatively simple catch.
The unearthing of past tweets this week have made Robinson’s first international match a chastening experience but he has impressed on the field and was the pick of the England bowlers to help to restrict New Zealand to 378.
Rory Burns justified his recall - having been dropped for the final two Tests in India last winter - with an encouraging 59 not out, in which he batted fluidly after a nervy start, as he and Joe Root (42no) led England to 111 for two at stumps.
The pair came together on 18 for two after Dom Sibley was adjudged lbw to Kyle Jamieson and Zak Crawley got the faintest edge to a booming heave off Tim Southee, with New Zealand’s probing seamers finding early movement that had eluded their England counterparts on Wednesday.
Root was given a thorough examination by the exacting Colin de Grandhomme, whose rising delivery thudded into the same right hand the England captain had taken a blow to earlier in the week in training. Root received some treatment and wrung his arm out a couple of times in the moments afterwards but he settled back down to his task.
Burns seemed all too eager to take on the pull against Neil Wagner, who had earlier impressed in a cameo with the bat as last man, but the left-handed opener and Root had to show caution in the final throes of the day to ensure they will resume their unbroken 93-run stand on Friday.
The day started with the spotlight on Robinson, 27, who apologised the previous evening for historical social media posts that used racist and sexist terms from 2012 and 2013, when he was in his late teens, that had surfaced on Wednesday and been shared online.
He was kept out of the attack as James Anderson and Broad were entrusted with a second new ball that was only six overs old, but the veteran pair were unable to stymie the runs as Henry Nicholls moved to an unobtrusive half-century before Conway brought up his 150 and then set a new record for the highest debut score in England.
Robinson was introduced into the attack to a welcoming reception from those in attendance inside the first half hour, but it was on the boundary rope where he first made an impact to help end a mammoth 174-run stand, pouching a chance at long-leg after Wood used his extra pace to hurry Nicholls (61) with a well-aimed bumper.
That opened the floodgates with BJ Watling thick edging a sharp chance to second slip after attempting to work Wood to leg while Mitchell Santner tamely chipped the paceman to short extra cover after Robinson had nipped one back up the slope to locate De Grandhomme’s pad, the original not out decision overturned on review.
New Zealand had lost four wickets for six runs as they lurched to 294 for seven while they were in real danger of sinking without trace when Robinson accounted for Jamieson after lunch, with the naggingly-accurate England seamer denied a five-wicket haul when Southee’s loose drive to mid-off was shelled by Broad, moving to his right.
Southee nicked off to Anderson as debuting wicketkeeper James Bracey gratefully accepted his first catch behind the stumps before last man Wagner (25no) played his part in a useful 40-run stand for the final wicket.
Wagner lofted Broad over long-off for six before driving Wood off the back foot for four - strokes that would have pleased any top-order batsman - before Conway moved to 200 exactly by pulling Wood over the long-leg boundary.
His epic 347-ball innings, containing 22 fours and one six ended in unfortunate fashion, run out at the second attempt by Root, as he was just unable to carry his bat in the first Test of this two-match series.