The Volts posted a competitive tally of 174 for eight. That looked like it might be enough, with Michael Rae producing a wonderful bowling spell for the home side.
He picked up the key wickets of Martin Guptill and Glenn Phillips to tip the game in Otago's favour, and finished with three for 23.
But some big hitting from Ronnie Hira (33 off 15) and Robbie O'Donnell (27 not out from 13) sealed a tense win for the visitors from the penultimate ball.