At lunch on the fourth day, England in their second innings were 175 for three -- 41 runs in front.
England skipper Alastair Cook was 69 not out and vice-captain Joe Root unbeaten on 58, with their unbroken stand for the fourth wicket so far worth 101 runs.
But given they were effectively 41 for three, England's difficulties were far from finished in a match where they have largely been outplayed in all aspects.
England resumed on 74 for two, 60 runs adrift, with Cook (32 not out) and Bell (29 not out).
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They had not added to their score when, off just the third ball of Sunday's play, Bell, trying to drive a Tim Southee outswinger, edged high through to Tom Latham, deputising for injured wicket-keeper BJ Watling.
England, in their first match since former captain Andrew Strauss was appointed their director of cricket and with Jason Gillespie reportedly waiting in the wings to replace the sacked Peter Moores as the team's full-time coach, now badly needed a decent stand between Cook and Root.
Cook's cut boundary against off-spinner Mark Craig then saw England into the lead.
Root -- out for 98 in the first innings -- swept Craig for four to post an 83-ball fifty including seven boundaries.
In the last over before lunch, Root, on 57, survived an 'umpire's call' review after missing an inswinger from left-armer Trent Boult.