Neesham's 107 helped the Black Caps to 508-7 declared in the first Test with the West Indies in Kingston, with the hosts 19-0 in reply at stumps on day two.
The 23-year-old made an unbeaten 137 against India in Wellington in February, and followed up his debut century with a patient knock that saw him face 171 deliveries and put on 201 runs for the sixth wicket alongside wicketkeeper BJ Watling (89).
Despite becoming the first Black Cap to score centuries in his first two Test matches, and the eighth player overall to achieve the feat, Neesham remained level-headed
"Obviously it's pretty pleasing to start well in your Test career, but on the other hand, that's all it really is - a promising start," Neesham told BLACKCAPS TV.
"So the main thing will be to go on from here, and keep putting performances on the board.
Neesham revealed he had worked hard with former Black Cap and current batting coach Craig McMillan, who joined the national set-up in May, on combating the threat of West Indies off-spinner Shane Shillingford.
"Over in the IPL, I wasn't playing a whole lot so that was a good opportunity for me to spend a lot of time playing spin in the nets, and working on strategies," he said.
"And when we came over to Montego Bay, I started working with Craig McMillan for the first time and we did a lot of talking, and a lot of acting around plans for especially the off-spinner (Shillingford).
"So it looks like it came to fruition."
Neesham conceded it was tough going for him and Watling early on day two at Sabina Park, before they guided NZ towards the 500-mark.
"Myself and BJ just talked about getting started, and getting a partnership going," Neesham said, of their plan prior to play starting.
"We knew from talking to the top-order batsmen that once you've faced 20 or 30 balls, then it starts to get a little bit easier to score."
West Indies left-arm orthodox tweaker Suliemann Benn appeared unhappy with the placid nature of the Kingston wicket.
Benn finished the first innings with figures of 3-142 from 52 overs, while Shillingford snared 3-145 from 46.3.
"I am not saying it is not a sporting pitch but it is very flat. Not a lot has happened off the pitch. We played two seamers and two spinners and there was not enough assistance for four bowlers," Benn said.
"I am not saying they (should) prepare pitches to suit the home team. I am far from saying that.
"I am just saying that you want something that is going to spin, going to seam (and) you can bat on it as well.
"That is a proper Test match pitch."