The Volts posted a modest 120 for eight. Opener George Worker paced the chase with a fine knock of 71 not out from 53 deliveries.
It was pretty much a lone hand, too, with Kruger van Wyk (12) and Dane Cleaver (17 not out) making a small contribution each.
The Stags remain in fifth place with 14 points. They will need to keep winning and for other results to fall their way to make the playoffs.
Otago (8 points) made the final last season but will have to settle for last place this summer, even if they win their final game, which is against Wellington (22 points) in Dunedin tomorrow afternoon.
It has been a miserable campaign for the Volts. They did well last night to scramble after a terrible start which saw the visitors slump to 35 for three and then 87 for seven.
Former Australian and Dutch international Dirk Nannes was left out of the playing XI. His spot was taken by Craig Smith, who played his first twenty20 game for Otago since January 2012.
Otago Boys' High School pupil Josh Finnie (17) made his debut. The all-rounder picked up two wickets with his off-spin and did not look out of place with the bat.
Roald Badenhorst injured his shoulder while diving to make his ground. He had his arm in a sling and did not field, so the prospects of him playing tomorrow would seem remote.
A minute's silence was observed at the beginning of the game for Australian cricketer Phillip Hughes, who died on Thursday from the injury he sustained when struck by a bouncer during a Sheffield Shield game.
Rain interrupted the match after just five deliveries of Otago's innings. An hour's play was lost and the game was trimmed to 17 overs apiece.
The Volts may have wished it rained for at least another hour or so because they had slumped to 35 for three by the sixth over.
Aaron Redmond chopped on, Michael Bracewell inexplicably stepped to off and was bowled around his legs for a duck, and Iain Robertson skied a catch to square leg.
It was a rather forgettable sequence for the visitors and Brad Rodden soon added to the woes when he scooped a drive to cover.
That brought Finnie to the crease. He boldly guided a delivery wide of the slips to collect his first runs - a boundary - in elite cricket. And he had the vastly experienced Ryan ten Doeschate down the other end for support.
Finnie had a life on eight when he gloved the ball over the diminutive van Wyk. Seth Rance has been bowling wonderful lengths this season and bowled a brilliant 14th over, putting pressure on the batsmen.
Finnie cracked. He looked to loft Rance into the onside and was bowled for 12.
The bowler then popped up in the outfield to take a regulation catch to dismiss ten Doeschate for 31.
The Volts' chances of posting a competitive total departed with ten Doeschate.
Rance was outstanding with the ball, taking two for 22 from four overs. He had good support from spinner Ajaz Patel, who took one for 11 from three overs.
