England need a further 210 runs to wrap up a series victory over New Zealand, having been set 258 to win after a brilliant century from former captain Kane Williamson.
Only three teams have ever lost a Test after enforcing the follow on, but England could join that list after New Zealand's much improved performance with the bat in their second innings.
Should England reach the target, it will be the second-highest successful run chase in Wellington behind Pakistan's 277 in 2003. But while it may be a challenging prospect for England, they did complete four even bigger run chases last summer including three against New Zealand.
Having been asked to follow on after getting bowled out for just 209 in their first innings, New Zealand's top order showed real resilience and quality. Openers Tom Latham and Devon Conway set the tone with a 149-run partnership, before Williamson took centre stage.
After getting dismissed for three single-figure scores in the series, Williamson was back to his best as he struck a 26th Test hundred and overtook Ross Taylor to become New Zealand's all-time leading Test run scorer.
His innings lasted more than seven hours and he shared important partnerships with Henry Nicholls and Daryl Mitchell that were worth 55 and 75 runs respectively, before Tom Blundell joined him in the trenches to help the hosts set England a challenging target.
Blundell made an impressive 90 to go with his excellent hundred in the first Test and has now passed fifty a total of six times in 11 innings against England. And with the pair in the midst of a huge 158-run stand, it was England's golden boy Harry Brook who made the unlikely breakthrough.
With just eight first-class wickets to his name, Brook's gentle seamers accounted for Williamson as he got caught down the leg side after looking almost imperious on his way to 132. From there, New Zealand's innings crumpled as they lost their last five wickets for just 28 runs, with Jack Leach picking up his fifth five wicket haul for England.
In response, England reached 48-1 at the close of play with Zak Crawley's lean run of form continuing when he was bowled through the gate by an excellent Tim Southee delivery. And things are set up for a fascinating final day's play as England hunt a historic victory and New Zealand look to level the series.
