Blackcaps talisman Kane Williamson is just four runs away from history, as his team battles to save the second test against England at Wellington's Basin Reserve.
The former captain will return to the crease on Monday morning, chasing former teammate Ross Taylor to become New Zealand's highest-scoring test batter. Taylor currently holds that honour with 7683 runs, while Williamson lurks just three behind at stumps on day three.
Already leading the way with 25 career centuries and a 52.90 average, Williamson, 32, has struggled for runs during the current series, scoring just 6, 0 and 4 in his previous three innings, but has hung around long enough to compile the 29 runs needed to surpass Taylor.
Dismissed for 209 in their first innings at the Basin Reserve, the home team were asked to follow on and reached tea at 128 without loss, still 98 runs short of making England bat again.
Williamson emerged from the pavilion, when opener Devon Conway was caught by close-in fielder Ollie Pope, off Jack Leach's bowling, for 61 - his seventh test fifty.
Williamson almost departed in identical fashion off the first ball he faced, with Pope a fraction slow to repeat his reflex snatch. He survived a review, when a delviery from part-time spinner Joe Root clipped something on the way through to the keeper, but replays confirmed it was Williamson's armguard.
By the end of play, he had compiled 25 runs, with Henry Nicholls on 18 at the other end and the Blackcaps on 202/3, still 24 runs behind England's first-innings 435/8 declared.
After reaching lunch at 40 without loss, Latham and Conway dominated the afternoon session, showing the form that has been sorely missed previously in this series. Latham became the seventh Kiwi to score 5000 test runs, bringing up his 26th half-century to sit on 72 not out at the break.
Conway struggled early, but reached his seventh test fifty, still there on 53 not out.
After tea, both openers fell short of centuries, with Latham reaching 83, before he was ajudged out leg before wicket, trying to sweep Root. Will Young did not last long, bowled by Leach for eight, but Williamson and Nicholls put on 35 runs to see their side to stumps.
Earlier, an allout batting assault from Blackcaps captain Tim Southee was unable to stave off the follow-on, as his team desperately tried to prevent an innings defeat.
Taking a leaf out of the 'Bazball' philosophy that has helped the tourists smother New Zealand, Southee smashed 73 runs off 49 balls - including six sixes and five fours - to get his side within a sniff of respectability, but they fell 26 runs short of their immediate target and were asked to try again.
Latham and Conway reached lunch relatively unscathed, steering the home side to 40 without loss. At the same stage of the first innings, New Zealand had already lost Conway, Kane Williamson and Will Young.
Beginning the day at 138/7, the Blackcaps were still 297 runs short of England's opening effort, with Southee on 23 and wicketkeeper Tom Blundell 25. The skipper had already shown his intent and continued where he left off in the morning session.
He and Blundell put on 98 runs for the eighth wicket, with Southee clearing the boundary three times in one Jack Leach over, before lobbing an infield catch to Zak Crawley, off Stuart Broad's bowling.
The dismissal left him four runs off his highest test score of 77 not out off 40 balls in his debut against England as a teenager in 2008.
Blundell followed seven runs later, caught by Leach, off Broad, then Matt Henry became the last to fall, unable to keep a short ball from Broad down and caught by Jimmy Anderson.
Latham and Conway did not always look comfortable in the pre-lunch period, but showed the starch that has been too often missing from the Blackcaps' batting efforts in this series.
England 435/8d
NZ 209 (Southee 73, Blundell 38, Latham 35; Broad 4/61) & 128/0 (Latham 83, Conway 61, Williamson 25no; Leach 2/59)
England lead by 24 at stumps
