After the dismissal of opener Matty Hurst, England pair Salt and Jos Buttler got Originals off to a decent start, taking their side to 49-1 after 26 deliveries.
But Originals breached the ropes on just four occasions from that point, as the Brave bowlers successfully throttled their opponents.
Mills was parsimonious while also accounting for Originals’ three most dangerous batters.
He had Buttler caught at deep cover from his second ball, and induced a leading edge from the big-hitting Heinrich Klaasen for a caught behind.
Having reached 60 from 39, Originals captain Phil Salt would have felt he was in a position to push on with 20 balls remaining.
He hit the next Mills delivery for four, but the Brave veteran struck again next up, sending down a bouncer Salt pulled to short fine leg.
Originals handed Hundred debuts to 43-year-old James Anderson and 17-year-old rising star Farhan Ahmed, but both went wicketless, with 24-year-old Currie the key bowler.
Anderson took the ball from the start of the Brave innings, but ex-England batter Jason Roy had his measure, hitting five boundaries off the veteran’s bowling, as Anderson finished with figures of 0-36.
Currie dismissed Leus du Plooy to end a promising 32-run second-wicket partnership, before removing Laurie Evans and later Chris Jordan and Michael Bracewell in the space of three balls.
His efforts seemed to have put his side on course to win, but the Brave tailed wagged to pull off a remarkable victory.