Early on Otago were in trouble at 83-4 after their top four were all sent back to the pavilion by Auckland seamers Chris Martin and Mitchell McClenaghan.
But all-rounders Nathan McCullum and Sam Wells steadied the chase for Otago as they put on a valuable fifth-wicket stand of 72 before McCullum was eventually dismissed for 77.
Derek de Boorder came and went for one run before Wells departed shortly after for 39 but left-hander Jimmy Neesham struck a few lusty blows to bring the visitors to victory.
Neesham, who has been in decent form this summer, belted 36 from 30 balls including six fours and a six, while paceman Neil Wagner held up the other end and contributed a valuable 17 as Otago finished on 223-7.
Martin finished with 3-62, while McClenaghan claimed 3-48 and Kyle Mills snagged the other wicket but they couldn't find a way to get their side over the line.