From 54-6 Luke Woodcock and Harry Boam commissioned a rescue operation for the visitors as they added 72 for the seventh wicket before Boam was eventually out for 35.
Woodcock ended up with the highest score of the innings as he was unbeaten on 40, while Otago seamer James Fuller picked up 4-24 from four overs.
Needing a shade above seven an over for victory, Otago got off to a rocky start as left-arm spinner Mark Houghton dismissed Hamish Rutherford (0) and Aaron Redmond (6) inside the first two overs.
Veteran opener Neil Broom steadied the chaos as he played the anchor role, while Derek de Boorder (33) and import Ryan ten Doeschate (21) blazed away from the other end.
When ten Doeschate was caught by Ronchi from the bowling of Ryder the Firebirds caught a sniff of an unlikely victory and when they ran out Michael Bracewell without scoring they believed they could off something special.
Broom eventually succumbed for 60, leaving Otago needing 14 from the final 14 balls but Ian Butler struck a few useful blows to see the Volts home as he finished unbeaten on 23.
The victory could be lucrative for Otago as they also earned a berth in this year's Twenty20 Champion's League qualifying stage.