Monty Panesar's Test best bowling figures of six for 37 on Sunday helped dismiss New Zealand for 114 in their second innings leaving England needing 294 to win the second Test at Old Trafford.
The highest fourth innings total to win a Test at Manchester is 231 by England against West Indies in 2004.
Left-arm spinner Panesar, who claimed his 100th Test victim before the tea interval, spearheaded the fight-back on day three of the match after England had earlier capitulated in their second innings to be all out for 202 and surrendered a first innings deficit of 179 runs.
Panesar exploited a pitch that offered him considerable bounce and turn as New Zealand's batsmen struggled to master his bowling. Opener Jamie How top-scored with 29.
New Zealand's left-arm spinner Daniel Vettori took five for 66 from the same end that Panesar was bowling earlier in the day.