The hard-hitting left-hander gave respectability to the Otago innings after the middle order crumbled to the steady Canterbury attack, led by right-arm swing bowler Matt Henry, who took three wickets for 29.
Neesham, who transferred from Auckland to Dunedin this year, batted with confidence and showed he could be a big asset to the Volts this summer.
Canterbury declared at its overnight score of 297 for three on the first day on Tuesday. Play was washed out on Wednesday.
Otago failed to establish an innings and was bowled out for 170. The only other batsman to make full use of the conditions was veteran Craig Cumming, who showed patience in scoring 48.
The former Otago captain batted steadily and stayed at the crease for 100min in a game that was a dress rehearsal for the first-class season that begins next month.
Cumming, who was the Otago captain from 2002 until last season, gave leadership to an Otago team that needed to display more patience.
Michael Bracewell (19), Hamish Rutherford (16) and Neil Wagner (13) all got starts but were not able to stay in long enough to establish a long innings.
"Another day on a grass wicket was valuable but a few of the guys were a bit reckless," coach Vaughn Johnson said.
The plan for the game was for Canterbury to bat throughout the first day on Tuesday and Otago to bat for the day yesterday.
"It was the opportunity for our batsman to have more practice with another knock after we were dismissed in our first innings," Johnson said.
• Bowler Kyle Mills will miss next week's one-off test with Zimbabwe and return to New Zealand following an injury to his abductor muscle, APNZ reports.
Mills picked up the injury in last week's first one-dayer and will undergo further scans on his return.
He will not be replaced.
Mills is one of the Black Caps' main strike weapons and his absence compounds that of Tim Southee, who missed the tour with a knee injury.
"Initially it was thought to be a strain but a scan has shown a slight tear to his abductor muscle," New Zealand manager Mike Sandle said.
"Clearly, it is disappointing for Kyle, who was looking forward to making a return to the test team. We wish him a speedy recovery and are hopeful he will be available for selection for the upcoming test series against Australia."
Meanwhile, New Zealand Cricket has reported a financial surplus of $2.6 million.
It is the first year in a new financial cycle following the ground-breaking eight-year partnership agreement between New Zealand Cricket, the New Zealand Cricket players' association and six major associations.
"In a year including an ICC Cricket World Cup, NZC expects to do well financially and it is heartening to see a good surplus posted, although it is lower than what was anticipated," chief executive Justin Vaughan said in the annual report.
"The US dollar continues to be challenging and revenues from the professional game were lower than usual, with just the solitary home series against Pakistan last season."
