With Jofra Archer out of the T20 World Cup, Garton sent a timely reminder to selectors with the important wickets of Dawid Malan Alex Hales and D’Arcy Short as the Rockets lurched to 31 for four from the 25-ball powerplay.
Figures of three for 18 from Garton were backed up by a miserly three for eight from fellow paceman Mills, who has been mentioned as a T20 World Cup bolter by England captain Eoin Morgan as the Rockets were skittled for 96 from 91 balls.
It was a total knocked off with ease under the Kia Oval lights, Paul Stirling hitting 31 and James Vince continuing his purple patch with 45 not out as the Brave overhauled their target with seven wickets and 32 balls to spare.
This was a bowling triumph for the Ageas Bowl-based Brave, who have both men’s and women’s sides in the final of the inaugural season of this competition, with Garton rising to the fore after the Rockets were invited to bat.
The Trent Bridge-based Rockets had beaten their opponents by nine wickets in the group stage but despite some occasional belligerence, only four batsmen reached double figures, with Samit Patel’s 20 off 21 their top score.
Malan made a punchy start but ultimately the Rockets were unable to recover from the cluster of early wickets as the Brave booked their place in the men’s showpiece, where they will play Birmingham Phoenix on Saturday at Lord’s.
Malan looked set to crown his recall to the England Test squad after a three-year-absence, tickling Garton fine before driving then pulling Craig Overton with authority for three successive fours, but his downfall marked a frenetic passage of play where the Rockets lost their first four wickets in the space of 15 balls.
Malan’s back-foot punch took the edge while Garton had his second caught behind in the same set of five when Hales, dropped low at point two balls earlier, also feathered through to wicketkeeper Quinton de Kock.
Steven Mullaney missed a big heave off Overton, who pegged back off-stump, and Short was surprised by one that seemed to stick in the pitch, splicing to midwicket as a fired-up Garton celebrated a third top-order wicket.
Patel and captain Lewis Gregory attempted to steady proceedings, the former clubbing left-arm wrist-spinner Jake Lintott over midwicket for the Rockets’ first six from the 45th delivery, but it was apparent scoring was a difficult prospect, with Mills particularly tough to get away.
Mills was in the wickets column when Gregory smeared to extra cover while Lintott took a supreme diving catch to his left at mid-off to account for Patel. Either side of the pair’s downfall, Tom Moores provided some light relief by crunching Lintott down the ground before pulling Overton over long-leg for back-to-back sixes.
Moores was undone by a trademark Chris Jordan slower ball, hammering to Overton in the deep, before Mills took a further two wickets to bring the Rockets’ innings to a premature end without reaching three figures.
A supreme bowling performance was needed from the Rockets but Stirling swept Matt Carter’s first ball for four and slammed a flat six over midwicket from his fifth.
The tone was set even though South Africa dangerman De Kock was bounced out for six by compatriot Marchant de Lange, who leaked fours either side of the wicket.
Rashid Khan conceded 14 runs in three balls off James Vince, including a big six over midwicket, while Sam Cook was deposited over long-on by Stirling to bring up the Brave’s 50 after 24 balls.
Stirling’s 19-ball cameo was ended when he holed out to De Lange, who took the catch at the second attempt running back from mid-off, but it was a rare moment of respite for the Rockets.
Alex Davies was caught behind off the pacey De Lange, a not out decision overturned on review, but Brave captain Vince was a calm presence and finished unbeaten on 45 off 27 balls, thumping his sixth four to get his side over the line to go with two sixes.