Neil Broom (45) and Neesham (52) got their innings on track but when they were dismissed Otago lost their way.
Nathan McCullum added 41 to offer some resistance but five different ND bowlers took wickets as they eventually bowled Otago out for 209 to book a 92-run win.
At the Hagley Oval in Christchurch, Wellington registered a thumping victory over Canterbury thanks to some career-best bowling by young seamer Scott Kuggeleijn.
The 21-year-old, who had been expensive during the first few rounds of the Ford Trophy, bounced back to form with 5-24 from 6.1 overs as he tore through the Canterbury top order.
Shanan Stewart top-scored for the home side with 41 but no other batsman passed 30 as Canterbury were bowled out for only 143.
They were lucky to even get that many as Wellington bowled an embarrassing 15 wides, with Mark Gillespie being the worst offender with six from nine overs.
Needing only 144 runs for victory Wellington made light work of their run chase as the in-form Michael Papps made 47 from 42 balls while Grant Elliott cracked 44 and Jesse Ryder added an unbeaten 38 as the Firebirds eased home by seven wickets in the 22nd over.
The day's most one-sided game was played at the Eden Park Outer Oval as Auckland accounted for Central Districts by 211 runs - their largest victory in a domestic one-day game when batting first.
The two Colins - Munro and de Grandhomme - again provided the runs as Munro made 78 while de Grandhomme blasted 60 from only 48 balls.
Auckland were bowled out for 285 in the 48th over as CD seamer Carl Cachopa picked up 3-35 but that total proved more than enough as the visitors were rolled for 74 - their third-lowest score in one-day cricket.
Kyle Mills (2-11), Chris Martin (3-33), Michael Bates (2-19) and de Grandhomme (2-9) did the damage.
Wicketkeeper Gareth Hopkins pouched six catches - the most by an Auckland stumper in a one-day game - which was made more impressive as Auckland only had to take nine wickets to register victory as Central Districts seamer Bevan Small didn't bat due to injury.
The next round of matches will be played on Sunday.