New Zealand pacer Tim Southee took six wickets but a painstaking hundred from England's Rory Burns pulled things back for the hosts in the first Test at Lord's on Saturday.
New Zealand were 62-2 in their second innings at stumps on the fourth day, a lead of 165 runs and in reasonable control of the opening match.
Ollie Robinson, continuing an impressive on-field debut, dismissed both fellow newcomer Devon Conway, fresh from his first-innings 200, and New Zealand captain Kane Williamson for a return of 2-8 in nine overs.
New Zealand, following Friday's total washout, had damaged their hopes of taking complete control of the Test by twice reprieving Burns before the Surrey left-handed opener completed his third Test century.
Burns was finally last man out for 132 to give veteran paceman Southee figures of 6-43 in 25.1 overs as England, in danger of following-on at 140-6, reached 275 – still 103 runs adrift of New Zealand's first-innings 378.
Williamson, however, is unlikely to make a declaration that could give England a chance to win ahead of both next week's series climax at Edgbaston and New Zealand's appearance in the inaugural World Test Championship final against India later this month.
England captain Joe Root fell for 42 to the first ball of Saturday's play when he edged a fine delivery from the towering Kyle Jamieson to Ross Taylor at slip.
England then lost three wickets for no runs in 21 balls in a middle-order slump, as Southee removed Dan Lawrence and debutant James Bracey for two of the four ducks in the innings.
Burns, watching the collapse from the other end, had started a sunny day seemingly ideal for batting on 59 not out.
It took Burns a further 133 balls to score the 41 runs he required to reach one hundred.