England’s second-wicket pair, both in need of significant contributions after uncertain starts to their Test careers, joined forces after another failure from Alastair Cook in a stand of 123 which helped the tourists to 202-3 and a lead of 231 by stumps on day three at Hagley Park.
They were consolidating back-to-form Stuart Broad’s 6-54 as New Zealand were bowled out for 278 to give England sound prospects of a series-squaring first win of their otherwise conspicuously unsuccessful winter.
Broad completed his first five-wicket haul in more than two years to earn England a narrow first-innings lead - and after all-time record run-scorer Cook then took his paltry series haul to just 23 in four innings when he fell to Trent Boult yet again, Vince (76) and Stoneman (60) took over.
Cook paid for a tentative forward push, edging behind, as the Kiwi left-armer did for him for the fourth successive time over the past two weeks.
On a fine pitch here, with pace, even bounce and just a hint of increasing help for spin, an intriguing contest was finely poised.
But Vince and Stoneman did enough to give England an evident advantage by the close.
The former has previously served up a succession of frustrating cameos, raising expectations with high-class timing only to fall in anti-climax too many times.
He began with a trademark cover-driven four from the second ball he faced, and on this occasion never looked back until he flashed an edge to slip off Boult and was well-caught by Ross Taylor seven runs short of his career-best.
Vince’s third Test 50 arrived just before tea, with another cover-drive off the leg-spin of Ish Sodhi for his ninth boundary, and Stoneman reached the milestone in early evening - with a cut over the top of the slips for his sixth four.
The left-hander was twice dropped in the slips off Colin de Grandhomme either side of his 50, and also had to overturn a review on 35 when Neil Wagner thought he had him caught-behind with one which hit only his shoulder.
Each batsman was bookending a tough winter which began with their twin 50s against Australia in Brisbane.
Stoneman’s hopes of a maiden hundred foundered when he edged another, going after Tim Southee without feet and brilliantly caught-behind by BJ Watling - this his top-score among five half-centuries - and when Vince went, too, England still needed some consolidation.
Captain Joe Root and Dawid Malan then took no chances in the final hour.
Broad’s fifth wicket had earlier come when Sodhi edged him behind for Jonny Bairstow’s fifth catch of the New Zealand innings.
But the hosts had grasped the early initiative as Southee hit 21 of 27 runs from 5.1 overs before the second new ball was available on the way to a 44-ball 50, containing eight fours and a memorable pulled six off Ben Stokes to go with his six first-innings wickets.
James Anderson then instantly struck with a brilliant outswinger to end Watling’s five-hour innings of 85 - and after he also bowled Southee, it fell to Broad to end Wagner and Boult’s last-wicket stand of 39 when the No 11 was well-caught by Malan at long-leg.
Second Test, Christchurch: England 307 (J M Bairstow 101, M A Wood 52, T G Southee 6-62, T A Boult 4-87) & 202-3 (J M Vince 76, M D Stoneman 60), New Zealand 278 (B J Watling 85, C de Grandhomme 72, T G Southee 50, S C J Broad 6-54, J M Anderson 4-76).