Watling's 100 not out took New Zealand to 338 for six in their second innings at stumps on the third day, with their lead also 338 after both sides made first innings totals of exactly 350.
It meant England would have to rewrite the record books were they to win this match and take the series 2-0 after their 124-run victory in the first Test at Lord's.
The most any England side have made to win in the fourth innings of a Test is the 332 for seven they posted against Australia at Melbourne back in 1928/29.
Australia, thanks to brilliant centuries by Arthur Morris (182) and Don Bradman (173 not out) made 404 for three for a celebrated seven-wicket victory over England at Yorkshire's headquarters in 1948.
And England themselves scored 315 for four, with Mark Butcher making an unbeaten 173, to beat Australia by six wickets in 2001.
Stuart Broad proved a thorn in the side of New Zealand with both bat and ball early on the third day.
Broad ensured first innings parity and then reduced New Zealand to 23 for two in their second innings.
That was the first of several fine stands in the innings, with Watling adding 121 with New Zealand captain Brendon McCullum (55) and 53 with Luke Ronchi (31).
South Africa-born Watling, playing as a batsman only in this match after he injured his knee keeping wicket at Lord's, went to his hundred in just under three hours off 136 balls, including 13 fours and a six, when he hooked James Anderson down to long leg for a single.
Broad's 46 helped England make 350.
He then took two wickets for four runs in 12 balls, with Tom Latham and Kane Williamson both caught behind.
McCullum became only the second New Zealand player, after retired former captain Stephen Fleming, to score 6,000 Test runs when a drive off Root beat the diving Wood at mid-off and went for four.
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