At lunch on the second day of the second Test, England were 54 without loss in reply to New Zealand's first innings 350 following some effective late-order hitting by the tourists.
Both Adam Lyth and fellow left-handed opener Cook were 27 not out. That left England captain Cook needing just five more runs to break batting mentor Gooch's England Test runs record of 8,900.
Meanwhile Lyth, on his Yorkshire home ground, had posted his highest Test score after he managed just seven and 12 on debut during England's 124-run win in the first of this two-Test series at Lord's.
Their total was all the more impressive as not only had they been sent into bat, but they had also collapsed to two for two as James Anderson became the first England bowler to take 400 Test wickets.
But Luke Ronchi marked his Test debut by top-scoring with a counter-attacking 88 and the wicket-keeper also shared a stand of 120 with Tom Latham (84).
Play resumed Saturday in sunny conditions and the fourth ball of the day saw Matt Henry pull all-rounder Ben Stokes to bring up New Zealand's 300.
But trying to repeat the shot next ball, Henry got a thin edge through to wicket-keeper Jos Buttler and was out for 27, made off just 21 balls including four fours and a six.
And when Stokes pitched up to Mark Craig, 14 not out overnight, the left-handed batsman drove him straight back over his head for six.
Craig also square-cut Stokes for four to raise New Zealand's 350. Last man Trent Boult eventually holed out to give paceman Broad figures of five for 109 in 17.1 overs.
It was the 13th time in 79 Tests that the 28-year-old Broad had taken five or more wickets in an innings.
Craig was 41 not out, with five fours and a six.
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