Cutting, 25, was released from Australia's limited-overs squad before start of play against Sri Lanka in Brisbane on Friday.
The potential match-winning seamer was immediately packed off to head for Perth in plenty of time for Saturday night's big clash.
Cutting had remained in Brisbane until close to the start of play as stand-by for recalled all-rounder Moises Henriques who was nursing a finger injury.
Cutting adds crucial bowling depth to the Heat with Perth boasting an imposing batch of former international stars though their top-order batting headlined by in-form ace Shaun Marsh, champion Mike Hussey and experienced Simon Katich.
Perth coach Justin Langer is in a selection quandry with confirmation the Scorchers will be without dashing veteran opener Herschelle Gibbs.
The South African batting great pulled a hamstring muscle early into his innings in Wednesday's thrilling win over Melbourne Stars.
Gibbs has been ruled out of any action for up to two months.
Langer and his advisors will ponder a recall for wicketkeeper Tom Triffit, or to play young all-rounder Hilton Cartwright in the biggest game of his short career or Marcus Stoinis.
Triffit, 22, was dropped to make way for Hussey's return from international duty against the Stars.
The revered international star was a surprise choice to take over the 'keeper's gloves.
Hussey also batted at number five in a typically influential cameo when the gifted left-hander belted an unbeaten 21 from just 12 balls to help his side over the line from the last ball of the most thrilling match in a short Big Bash history.