It was Otago's defence that first came to the fore, shutting down the hosts in the first half to prevent their possession advantage from translating into points.
A dominant scrum gradually put the visitors on the front foot, winning penalties to gain field position and allowing the outstanding Josh Ioane to put his side in front from the tee.
It took most of the first half before Otago grabbed the game's first try, with Josh Hill crashing over from close range to give his side a 10-point halftime lead.
But with the wind at their backs in the second spell, Otago quickly increased that edge to a match-winning margin.
Sam Gilbert was the first to find the line after the break, being sent clear by Kayne Hammington's smart pass, before Vilimoni Koroi collected a clever kick from Ioane to score the pick of the tries.
Manawatu earned a brief reprieve through Brayden Iose after Otago had coughed up possession near their own line, but Freedom Vahaakolo soon put away the game.
The wing gave his side an unassailable lead when he showed his pace to collect the ball from a scrum and race clear, before demonstrating his elusiveness with a stunning run down the right touchline and under the posts.
Manawatu 16 (B Iose, J Maraku tries; S Cruden 2 pens)
Otago 44 (J Hill, S Gilbert, V Koroi, F Vahaakolo 2 tries; J Ioane 3 pens, 4 cons, C Millar con)
Halftime: 3-13