Marcus Stoinis and Nikhil Chaudhary attempted to rebuild but managed only a cautious recovery before Cook found another edge, Salt completing his third catch of the innings to leave Brave at 45 for 3 at the halfway stage
The Australian all-rounder struck a 35-ball half-century and briefly threatened to lift his side to a competitive total before Sam Cook returned to dismiss him, finishing with excellent figures of 3 for 14.
Brave eventually finished with 115 for 8, the lowest total in their Hundred history, with Short picking up a couple of wickets as well.
Having elected to bowl, Welsh Fire’s experienced seam attack made full use of the conditions.
Scoring remained difficult as the ball continued to seam around.
Rachin Ravindra then tightened Fire’s grip on the contest.
Extracting sharp turn from the surface, the left-arm spinner removed Tristan Stubbs and Moeen Ali off successive deliveries.
With wickets falling regularly and boundaries proving scarce, Southern Brave struggled to build momentum.
Stoinis alone managed to break the shackles.
There was early hope of a defence when Jofra Archer dismissed Salt cheaply and conceded nothing until his eighth delivery, but Fire resisted any panic.
Short and Root instead focused on putting together a measured 56-un partnership that steadily shifted the chase in Fire’s favour.
Judging the conditions superbly, he mixed calculated aggression with smart strike rotation, using the scoop and ramp effectively against the pace bowlers.
He reached his fifty from 37 deliveries before finding an ideal partner in Tom Kohler-Cadmore, whose unbeaten 23 ensured there were no further alarms.
