In New Zealand's favour, only Australia's 1948 Invincibles (404 for three with Arthur Morris 182 and Don Bradman 173) have chased more to win in the fourth innings at the ground.
However, the pitch has suffered little wear and tear with six sessions left, albeit with rain forecast to intervene tomorrow afternoon.
New Zealand have won four tests in 53 attempts in England. A win this time would be their second at Headingley and continue a run of six undefeated test series.
Extraordinarily, under the International Cricket Council's rankings system, they will still drop from third to fourth if they tie the series.
Regardless, wins in England are significant.
One is reminded of the first win in England, also at Headingley in 1983. Wisden reported team member Jeremy Coney, a commentator at the 2015 edition, saying: "The main feeling was thinking of all the New Zealand players who have been coming here for 52 years, better players than myself, and making sure their sweat and effort had not been in vain."
A photo of that elation is captured in front of the pavilion as few players look at the camera while all manner of beverages are swilled.
The incumbent New Zealand side put up a batting display paced at 4.50 runs an over which captivated a Yorkshire-heavy Sunday crowd, and England bowling coach Ottis Gibson.
"The advantage lies with New Zealand. We have been unable to contain their attacking brand of batting.
"I was thinking 'the one-day series hasn't started yet, has it?' I don't know what to think of it, the way they bat.
"We attacked from a good length but under pressure you tend to drag it back a bit and not try to hit the top of off stump."
New Zealand opener Martin Guptill, who made 70 in the second innings, said they tried to play as positively as possible.
"At two-for-not-many [23], Ross [Taylor] brought impetus to the innings with a boundary off his first ball [on his way to 48 off 48 in a 99-run third wicket stand]. I fed off him. We ran well between the wickets, rotated the strike, put bad balls away and set the day up for B-J and Brendon [McCullum].
"B-J played beautifully. He came in, fought hard and played a fluent innings. You're not going to see too many better than that. 141 for four was a tough spot to be in.
"Timmy [Southee] also bowled well [to get four for 27 in 10 overs with the second new ball]. He's world-class and hard to get away when he gets the ball swinging. We pride ourselves on catching in pressure moments, especially those two that Mark Craig took to get rid of dangerous players [Ian Bell and Ben Stokes].
"The pitch is getting tougher to bat on. A few balls kept low and a few went through over the top [of the stumps]. Hopefully our bowlers can exploit that."
