Led by the Black Caps all-rounder's 131 runs and Hamish Rutherford's 79, Otago reached stumps at Nelson Park on 330 for seven from 96 overs.
Neesham's third ton for Otago included 13 fours and two sixes, and was a timely confidence booster before New Zealand's test series against Australia across the Ditch next month.
He brought it up with a single from the 105th ball he faced, before eventually being dismissed by Doug Bracewell eight overs from stumps.
Coach Nathan King praised Neesham's innings, calling it a ''really good'', chanceless knock.
He also saved some praise for Rutherford and Sam Wells, who scored 62 runs and shared a 157-run fourth-wicket partnership with Neesham.
King said the pitch was a good surface to bat on and hoped his side could push on beyond 400 today.
''It's hard work for the bowlers to get wickets, I'm not going to lie,'' he said.
Captain Rutherford won the toss and elected to bat. He and new Otago signing Brad Wilson put on 43 runs for the first wicket.
Rutherford dominated the partnership, scoring 32 of the first 34 runs in the morning session at a good clip.
Wilson, who managed just seven runs from 45 deliveries, became 18-year-old debutant Josh Clarkson's maiden first class scalp when he edged a delivery to Central Districts captain Kruger van Wyk in the 15th over.
That reduced Otago to 43 for one and brought Ryan Duffy to join Rutherford at the wicket.
They brought up three figures for Otago inside 28 overs, before Duffy (12 runs) was unluckily caught and bowled from the last ball of the session by part-time spinner Tom Bruce, whose full toss was smacked into the short mid-wicket fielder, before ballooning into the air for Bruce to catch.
Resuming on 101 for two after the lunch break, Rutherford only lasted two balls before falling to Black Caps bowler Doug Bracewell, caught and bowled for a well-hit 79 from 89 deliveries.
Neil Broom's first innings for Otago after a year playing for Canterbury lasted only five deliveries. He was bowled by medium pacer Andrew Mathieson for one to leave Otago struggling at 113 for four shortly after lunch.
But Neesham and Wells knuckled down and saw the visitors through to the tea break with 209 runs on the board and no further damage done.
Nick Beard (six runs) and Adam Miles (eight) will resume Otago's innings when play gets under way at 10.30am today.
Taieri bowler Jack Hunter is making his first class debut in the match, leaving Green Island seamer Dion Lobb to carry the drinks.
