Martin claimed 4-43 and Neil Wagner 4-42 to bowl the tourists out for a paltry 167, their lowest total batting first against the Kiwis.
Jonathan Trott made 45 but he was one of a clutch of batsmen to perish to reckless strokes.
Rutherford’s unbeaten 77 led the hosts to 131-0 by the close – trailing by 36.
He will resume on day three alongside Peter Fulton, who is 46 not out, as New Zealand – ranked above only Bangladesh in the International Cricket Council standings – aim to build on a position of strength that few would have predicted before play.
On their first Test outing in a hugely important year which sees them contest two Ashes series, England produced a batting performance that must rank among their worst in recent times.
Martin, the 32-year-old left-arm spinner, was gifted four of the cheapest wickets imaginable as England’s batsmen, with the exception of Trott, showed an alarming lack of application on a placid surface.
The assured Rutherford – son of former New Zealand batsman Ken – demonstrated the error of their ways with an innings that suggests he has a bright Test future ahead of him, while Fulton overcame a scratchy start to help blunt the six bowlers England employed in the final session.
England’s display will raise inevitable questions about their preparation for this series, which featured a solitary first-class match against a New Zealand XI, particularly given that only once on the last 13 tours have they won the opening Test.
However, their downfall at the University Oval lay in shot selection rather than execution, most notably when Matt Prior, Jonathan Trott and Stuart Broad perished during a frantic 22-ball spell which reduced them to 119-8.
Little England did impressed from the moment Nick Compton, defending tentatively, played on to Tim Southee in the third over of the game, which was delayed 24 hours following the first-day washout.
Alastair Cook, normally such an assured presence at the top of the England order, was not above criticism himself. He cut tamely to point off Wagner, who swung the next delivery back in to trap Kevin Pietersen palpably lbw.
A recovery of sorts was cut short when Ian Bell drilled a Wagner half-volley straight to Rutherford at short extra-cover, before Trent Boult – one of three left-armers in a four-man New Zealand attack – had Joe Root caught at third slip as he fenced at one slanted across him.
Martin claimed three wickets in two overs after lunch, all courtesy of needlessly aggressive strokes. Prior cut a long hop to point, Trott top-edged a rare sweep to short fine-leg and Broad holed out on the square-leg boundary when Martin again dropped short.
Finn and Anderson swung lustily in adding a much-needed 47 for the ninth wicket, but Finn’s dismissal – he perished on the pull the ball after Rutherford had been moved to deep square-leg – summed up England’s muddled thinking.
Anderson’s miscued swipe at Martin in the next over completed England’s misery with the bat, but Rutherford and Fulton ensured more was to come in the field.
Rutherford, 23, opened his Test account with a punched four wide of mid-on off Anderson, a shot typical of the aggression he showed en route to a 65-ball half-century.
He was dropped on 52 and 64, Broad spilling a tough low chance in his follow-through and Pietersen shelling what should have been a regulation catch at gully.
It was symptomatic of a day in which England’s cricket left much to be desired.
Reprinted from BBCnews