When speaking to BBC Sport, Leach gave short shrift to the idea that a fourth-innings chase of this size was not part of the plan.
"Why not?" Leach answered, before being asked if the original focus was on finishing the game within three days rather than keeping all results on the table going into the final day. "Well, yeah, obviously - you're always trying to win as quickly as you can. But that's not always going to be the case."
"Thinking back to Barbados, that [second innings in Wellington] felt a lot harder," Leach said. "Out here it has taught me a lot about how to get what you want out of a pitch, you have to work extremely hard. That is something I will massively take forward into the future. Sixty overs out there felt a lot harder than 69 in Barbados.
"[I was] Pleased with how I kept going. Not pleased with a lot of things as well but just happy we have a chance to win the game tomorrow.
"We're very confident to chase it down. We know how we want to go about our chases. It is a case of us sticking to our process, trusting that will work. It will be an exciting day."
"I feel like I have come on a lot and Stokesy has talked to me about wanting to challenge me in lots of different situations. That is going to help me"
Leach reflects on his cricket this winter
He credited the team for sticking with it throughout, even though there were times when it seemed that England were running on fumes and were slowly being flipped onto the wrong side of the game, notably during a 271-ball partnership between Williamson and Tom Blundell which added 158 to the score.
"Stokesy said [at tea to] give everything you have got. He put it a lot better than that.
"Sometimes it is just hard graft. You have to keep going, give that bit more and enjoy the graft rather than worry about things not happening; that was the message - enjoy being out there, you are playing for England and trying to win a Test match. What we have seen is the more we enjoy it the better we play. It worked."
Reflecting on his winter, Leach admits to being conflicted but believes there are positives, and negatives to improve going forward.
"It has been a mixture," said Leach. "I feel like I have come on a lot and Stokesy has talked to me about wanting to challenge me in lots of different situations. That is going to help me. Him putting me in those situations is really helpful.
"I feel I have learned a hell of a lot and things I will take forward - how I prepare, thinking about county cricket and longer spells. [The] Wind here - I found that difficult at times. All these things are good to experience and makes you realise how you can up your practice because you need to be stronger for longer.
"I was happy with how I bowled yesterday but pulled up tired today. From speaking to Jeets [Jeetan Patel], someone who had a very strong action and could keep going bowling long spells, if the opportunities are not there in certain games, it is about me using that in my practice. A real good learning curve from me."
Vithushan Ehantharajah is an associate editor at ESPNcricinfo