The visitors actually dominated possession and territory but produced a sloppy effort out wide.
Auckland pounced on Otago's errors and added a penalty try from a scrum late in the half to lead 21-0 at the break.
Salesi Rayasi skipped through close to the ruck to extend the lead early in the second spell and Otago was left with too much to do.
It scored a couple of consolation tries late when Auckland's discipline faltered.