New Zealand 229 for 3 (Conway 80, Young 82, Taylor 46*, Broad 2-22) trail England 303 (Lawrence 81*, Burns 81, Boult 4-85) by 74 runs
New Zealand boasted an embarrassment of riches for a second day running as Devon Conway and Will Young frustrated England's bowlers and moved to within 74 runs of England's first-innings total with seven wickets in hand at Edgbaston.
Conway, who cemented his place in the side with 200 on debut in the series opener at Lord's, produced another valuable, though not chance-less, innings of 80. And, while he would have been disappointed not to press on to triple figures again, a gutsy 82 from Young - in the side as a replacement for injured captain Kane Williamson - mitigated the damage.
Stuart Broad bowled superbly for his 2 for 22 from 15 overs, including six maidens, but he was the only England bowler to reap any reward for his considerable efforts - until Young's dismissal by part-time off-spinner Dan Lawrence on the last ball of the day.
England had resumed on 258 for 7 with Lawrence on 67 and Mark Wood 16. Wood provided serious entertainment as he pushed his score up to 41. He hit Trent Boult for three fours in six balls across two overs followed by back-to-back boundaries off Matt Henry as he punished New Zealand's persistence with short-pitched bowling.
Wood eventually fell, bowled by a Henry outswinger which found an inside edge onto the stumps.
Lawrence remained not out 81 to share top-scoring honours for England with Rory Burns, while Boult polished off Broad and James Anderson to end as New Zealand's leading wicket-taker with 4 for 85.
When Broad had Tom Latham, New Zealand's stand-in captain, out lbw in the sixth over of the innings, the visitors were 15 for 2.
Young ground out eight runs from 45 balls to begin with before settling into his stride, unfurling a beautiful on-drive to the rope off Olly Stone and then lacing another past third slip. In Stone's next over, Young jabbed another four through point, his feet leaving the ground as he latched onto a short ball.
Having survived on seven when Joe Root juggled and dropped a standard-looking slips catch off Stone's bowling, Young brought up his maiden Test fifty with a single off Anderson's late-moving inswinger.
Conway had earlier done well to make it back to his crease when Latham struck a Broad delivery straight back down the pitch and the bowler, following through, managed to get his fingers to it before it crashed into the stumps at the non-striker's end. Conway, who was advancing, tracked the ball like a hawk and managed to turn and stretch his bat back to safety.
That was positively skilful, whereas his next nervous moment - on 22 - fell more in the lap of fortune. Having edged Broad towards Zak Crawley at third slip, the soft signal given on the field was not-out, suggesting the ball had touched the ground first. Broad was incensed but, upon review, there was enough doubt for the decision to stand - and spark debate over the existence of the soft signal.
Conway and Young put on 122 runs together before Conway holed out to Crawley at deep backward square leg, giving Broad his second wicket, having conceded just 18 runs to that point midway through his 12th over. Conway's scores of 200, 23 and 80 meant he had scored more runs in his first three Test innings than any other New Zealand batter.
Broad gave Ross Taylor a thorough examination, beating the bat on numerous occasions while Anderson provided excellent support from the other end. It was Anderson who had Taylor given out lbw shortly after Broad had wrapped up his spell but the decision was overturned on review, which showed the ball was missing leg stump by a distance.
Taylor managed to grit his way towards a half-century and was 46 not out at stumps when part-time off-spinner Lawrence finally broke through in the last over of the day. Lawrence ended Young's knock with his ninth ball, finding an inside edge onto the pad, which Ollie Pope swallowed diving forward at short leg.
Young was playing just his third Test - he earned both his previous caps in the home series against West Indies in December - and had scored two centuries in three innings for Durham in the County Championship in the lead-up to this match, earning his place among six changes to the New Zealand side which drew at Lord's. Based on his performance at Edgbaston, he gave selectors plenty to think about going forward.