Otago won through its desire on defence, and its ability to stay in the game when almost under siege during periods of the first half.
Tasman had a monopoly of ball in the opening 30 minutes, but Otago hung tough and, in the second half, it pulled away, scoring five tries, all by backs.
The win gives its four wins from six games, and has it sitting in second position in the ITM Cup Championship.
The team was forced to back up from a game five days ago and started like it was feeling the effects of that 50-point romp over North Harbor.
Otago coach Tony Brown acknowledged energy levels were not quite there and went to his bench after 35 minutes sending on hooker Shota Horie and flanker TJ Ioane, for Sam Anderson-Heather and Lee Allan.
"Lee and Sam have been huge for us in the last two games but I felt we needed something out there to change things," Brown said.
"When our energy levels were low we just needed a spark and those guys brought it to us."
The team may have scored the five tries to Tasman's two efforts but Brown credited the win to his side's defence.
"Defensively, it was a big effort from the boys. Defence creates a culture and I have to be proud of the boys and the guts they showed out there."
Head of the queue in leading the Otago cause was pocket-rocket Japanese halfback Fumiaki Tanaka.
He was all over the park, leading attacks and also moving the ball on quickly to find space outside him.
"He is a world-class player and gives so much influence to our young guys. He wants to play Super 15 and I think a few franchises would have a look at him."
The win is Otago's third under the roof in as many games so far this season, racking up 134 points and scoring 15 tries.
"We love this place. This is the way we want to play the game, playing attacking football and moving the ball. We want to entertain the crowd and make them want to come and see us."
Otago's second half won it the game after it trailed 13-10 at the break.
Winger Marshall Suckling scored a try a minute into the second half after a chip kick from Tanaka and he scored again eight minutes later after the Tasman backline defence was stretched.
Tasman started to fade and, 14 points down, tried to push the pass with five minutes to go and Otago fullback Tony Ensor intercepted the ball and ran 50m to score under the bar.
He was then replaced by Peter Breen who scored the final try for Otago as Tasman put up the white flag.
It had made a lightning start, scoring after 30 seconds through skipper Andrew Goodman.
Otago was struggling to keep up and making errors at vital times.
It eventually got on the board with a Hayden Parker penalty.
Hayden Cripps then scored for Tasman and it looked ominous for the home side.
But Otago came back into the game five minutes before the break when winger Buxton Popoali'i threw the ball into himself from a quick lineout and proceeded to carve through the Tasman defence.
The ball was shifted wide and centre Jayden Spence dived over to score.
Parker, who enjoyed a fine day with his boot, kicked the difficult conversion from the sideline.
Apart from Tanaka, other stand-outs for the home side were lock Tom Franklin, and prop Liam Coltman. Horie was busy throughout.
Tasman rather went off the boil as the game went on and it had some weary legs at the end of the game.
Dunedin referee Adam Morrison went on to referee the final 25 minutes of the game, making his first-class debut, as Glen Jackson was forced off because of a hamstring injury.
ITM Cup
The scores
Otago 39
Marshall Suckling 2, Jayden Spence, Peter Breen, Tony Ensor tries; Hayden Parker 4 con, 2 pen
Tasman 13
Andrew Goodman, Hayden Cripps tries, Cripps pen
Halftime: 13-10 Tasman
Crowd: 4000.
