The 22-year-old Otago all-rounder scored his maiden first-class century to help his side fight back from 71 for five to reach 298.
Northern, which limped to 204 in its first innings, shared the day's honours, clawing back the 84-run deficit to be 120 for two at stumps on day two of its Plunket Shield match in Hamilton.
But Neesham was the individual star with a fine innings of 124.
The tall left-hander hits the ball as cleanly as perhaps even Jesse Ryder. And he certainly swats boundaries with the same ease.
His 100 came off just 121 balls and it featured 18 fours (72 runs).
Fittingly, he reached the milestone with another four, clipping a delivery from Brent Arnel off his pads through to the square leg boundary.
"It was a bit of a relief when I realised it was going to the boundary and that I'd got there," Neesham said.
"I put a little fist pump in and started to get the lid off."
The 90s passed painlessly.
Before the nerves had time to build he had flicked the shot through square.
"It all felt a bit easier than I thought it would," he confessed.
Neesham had joined Volts captain Derek de Boorder at the wicket with Otago struggling at 42 for five.
It was the sort of situation where the team expects those in the middle to resist temptation and just get through to stumps with no more damage done.
Neesham, though, was also under instructions to play his normal game and rushed through to 27 by stumps.
"I've been talking a lot to guys like Ian Butler and Aaron Redmond about how to go about batting in four-day cricket and the main thing is to stay positive and to try and keep playing my shots.
"There is no point trying to curtail it too much. The ball was moving around a wee bit, though, so the main thought was to try and get through to stumps and try and rebuild again in the morning."
The pair added 137 for the sixth-wicket before de Boorder was undone on 37. Neil Wagner chipped in 23 and Ian Butler whacked four sixes and six fours for an undefeated innings of 61.
Last man in, Jacob Duffy, did his best to hold his end up while Butler went on the attack. Duffy scored just two runs in a valuable partnership of 55 for the last wicket.
Arnel had bowled superbly on Sunday, taking four quick wickets. He eventually picked up the wicket of Mark Craig to snare his eighth five-wicket bag. He also captured his 200th first-class wicket when he removed Michael Bracewell on Sunday.
Legspinner Anton Devcich picked up two quick wickets to help wrap up Otago's innings.
At Nelson Park in Napier, Carl Cachopa posted his highest first-class score, an undefeated 179, to help Central Districts reach 430 for nine declared. In reply, Auckland was 80 for four at stumps on day two.
