The Sixers were unable to stop danger-man D'Arcy Short, who led Hobart to their fifth win from five starts this season.
Short hit 64 from 42 balls to chase down the Sixers' 8-161 with one ball to spare.
Hefty blows from veteran George Bailey (30 from 17) got the Hurricanes into a position where they needed just five off the final over by Ben Dwarshuis.
But Bailey was caught on the second ball of the last over to a diving effort from Moises Henriques setting up a tense finish.
Hobart snuck a two and single before Simon Milenko hit a leg-side boundary on the penultimate ball to secure victory.
Short was bowled by Sean Abbott (2-29) in the 15th over but his side did enough to get home.
Earlier, Daniel Hughes' top scored with 61 from 40 balls and shared a 67-run stand with Henriques to rescue the Sixes from a precarious 2-27 during the powerplay.
Hurricanes spinner Johan Botha inflicted early damage on his former side, removing both openers to finish with 3-22 from his four overs.
Botha returned in the 15th over to have Hughes caught in the deep when the Sixers were looking to launch.
Henriques (31 from 24 balls) looked in good touch before he was run out by a piece of brilliance from Short off his own bowling.
Hughes and Henriques tried to sneak a bye after Matthew Wade fumble but Wade recovered, flinging the ball to Short who backhanded the ball onto the stumps.
Former Australia limited over players James Faulkner picked up 3-26.