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.
Earlier in the day, Auckland began their second innings at 118-5 and pushed through to 274 to set Otago their total.
The in-form Colin Munro was again busy with the bat as he smashed 118 from 124 balls for Auckland, although no other player managed to pass 38 and they probably needed to set Otago a total closer to 300 on the Eden Park Outer Oval wicket.
At Seddon Park in Hamilton, Northern Districts require 10 wickets, while Canterbury need to make 403 runs to record an unlikely victory tomorrow.
The home side began day three today on 116-3 and went about racking up a decent second-innings total as opener Joseph Yovich scored 128, while he had strong support from Daryl Mitchell (73), BJ Watling (68 not out) and Corey Anderson who was unbeaten on 69.
Their total of 410-5 declared left Canterbury with a pursuit of 425 for victory and openers George Worker (14) and Peter Fulton (eight) finished the afternoon unbeaten before rain interrupted play.
ND are yet to register a win from their opening three Plunket Shield encounters and they will hope the bad weather can stay away tomorrow as they look for their first victory of the season.