In the first of three one-dayers against India A, he took just 48 balls to post 79 as the Kiwis made 308-6 after being sent in at Bay Oval in Mount Maunganui.
The all-rounder came into this series on the back of a strong Ford Trophy campaign, where he scored two hundreds as the Wellington Firebirds were crowned champions.
The visitors reached their target of 309 with an over and four wickets to spare, on the back of an unbeaten 80-ball 87 from Vijay Shankar.
Also impressing with the bat for NZ A were opener Hamish Rutherford, who made 70 off 66 balls, and wicketkeeper Tim Seifert, who made 59 off 53 balls.
When Will Young was dismissed for 32 at the end of the 33rd over, they had reached 151-4, then proceeded to add 157-2 off the last 17 overs of the innings, scoring at over nine runs per over.
The uptick was fuelled by Neesham and Seifert, who shared in a partnership of 82 runs off 67 balls.
Neesham increased his scoring rate once Seifert departed, caught at short fine leg, smashing 53 off the final 20 balls of his innings.
India A got off to a flyer in their chase, only losing their first wicket in the 10th over, once they already had 61 on the board.
Neesham was the most economical of the Kiwi bowlers, taking 1-40 from eight overs.
Hamish Bennett took 2-65 from his 10 overs, the wickets coming in the space of three balls to remove set batsmen Manish Pandey (42) and Shreyas Iyer (54) in the 26th over of the chase.
Shankar and Ishan Kishan established a strong partnership at that point, adding 116 for the fifth wicket to tilt the game in India A’s favour.
Lockie Ferguson also took two wickets but was expensive, conceding 75 from his 10 overs.
The second match of the series is on Sunday at the same venue.