Sangha and David Warner powered the visitors to 0-97 after 10 overs at Bellerive Oval on Monday night, allowing the Thunder to dream at the halfway mark of potentially a monster tally.
Regrouping, the minor premiers showed their class, led by Canes skipper Nathan Ellis.
Ellis arrested Sydney's run with two wickets in two balls - and almost a hat-trick - in the 11th over, including Warner (48 off 32).
Sangha marched on (67 off 42) before also falling to Ellis (3-23), the pick of the bowlers after failing to concede a boundary all night.
Captain Nathan Ellis starred with the ball for Hobart, taking 3-23. (Linda Higginson/AAP PHOTOS)
Riley Meredith (3-27) went for 16 in his second over but added the wickets of Sam Billings and Oliver Davies in the penultimate over as the Hurricanes' squeeze kept the chase in check.
A final over 14 off the below-par Chris Jordan (0-48) allowed Sydney to post what was a competitive tally, even though the ground favours chasing sides.
Fresh off a 35-degree day, a sell-out Hobart crowd clad in Hurricanes purple cheered their team in the hope of breaking their BBL duck.
The Thunder, looking for their second championship, would also be the first to complete a rags-to-riches turnaround of wooden spoon one season, winners the next.
Veteran David Warner contributed 48 off 32 balls for the Thunder. (Linda Higginson/AAP PHOTOS)
After the visitors were sent in to bat at a venue where the minor premiers have a 6-0 record this season, Sangha showed no fear to race to 24 off 10.
Warner was slower away but showed rapid pace between the wickets in an imperious opening partnership that fell just three runs short of a century.
The 38-year-old upped the ante but became Ellis's first victim, edging a slog to Matthew Wade, who caught well.
Purple haze: Hobart fans turned out in force at Ninja Stadium. (Linda Higginson/AAP PHOTOS)
Matthew Gilkes lowered his colours a ball later, dangling his bat and playing on for a golden duck, before Sam Billings almost gave Ellis a hat-trick by prodding at a ball that landed just shy of Tim David at mid-off.
Billings played a fine cameo (20 off 14) but this was the Sangha show, the 25-year-old - who made 151 at this ground on Sheffield Shield duty last month - rattling through to the 16th over before holing out.
Late shows from Davies (26 off 19) and Chris Green (16 off 9) pushed the Thunder to a strong position at the innings break.
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