The visitors led 13-7 at halftime - a converted try to Tony Ensor and a brace of penalties by Peter Breen against a converted try by Tasman's Peter Samu.
In the second half, captain Shane Christie scored a brace of tries for the home side, to go with a five-pointer to Mitchell Scott.
In reply, Otago crossed the line through Matt Faddes and No 8 Mika Mafi before Tasman's Trent Renata scored a late try to seal the victory.