Harbour's handling was sloppy, and they also gave away a slew of penalties during the first half which invited Otago into the game.
There were flashes of positives, and it would be unfair to write a team off after the first week of a competition, but Jackson has it all ahead of him if he wants to turn things around.
Few teams play with such a carefree nature as Otago, and their indoor home ground facilitates their attacking brand of rugby as conditions are never a concern.
Harbour grabbed the first try of the game after a scrappy beginning, with wing Tevita Li crossing, but they weren't able to hold onto the lead for long.
Flying Otago wing Fa'asiu Fuatai may score plenty of tries in his professional rugby career but few will top his first of the afternoon as he finished a beautifully-worked backline move for the home side.
Otago had a healthy lead after he completed his double, but the visitors cut into that as James Parsons scored and Otago took a 20-14 advantage to the break.
Scoring was muted in the second spell as the game trotted along at a steady clip but when flanker James Lentjes celebrated his Otago debut with a late try, the result was confirmed.
Harbour face a quick turnaround as they host Southland in Albany on Thursday night, and Otago travel north to meet Counties Manukau in a Ranfurly Shield challenge in Pukekohe next Saturday.
Otago 28 (Fa'asiu Fuatai 2, James Lentjes tries; Hayden Parker 3 pens, 2 cons) Harbour 14 (Tevita Li, James Parsons tries; Daniel Halangahu 2 cons). HT: 20-14.