Set 130 to win, the Australian wicketkeeper-batter quickly got on top of the Welsh attack at Cardiff, playing the leading role in an opening partnership with Sophie Dunckley.
The pair put on 73 before Dunkley picked out Aussie Heather Graham in the deep but by then Rockets needed only 57 more from 60 balls.
Joined by Nat Sciver-Brunt in the middle, Mooney brought up her 50 from just 27 balls before falling for 57.
Welsh Fire suffered a slow start, not helped by losing Aussie opener Georgia Voll for 18, caught by Mooney just as she seemed set for a big score.
In the day's other match, MI London and London Spirit have played out a thrilling tie after last-gasp heroics from Hayley Matthews and a crucial spell of tight bowling by Australian all-rounder Nicola Carey.
Hosts MI London, formerly the Oval Invincibles, were able to post 4-151 after Melie Kerr struck 49 not out, producing seven fours in an assured innings before Chinelle Henry produced fireworks with an unbeaten 33 off 12 balls.
After Marizanne Kapp claimed 2-24 to restrict MI London to 4-151, Spirit lost Aussie Grace Harris to a golden duck before Amy Jones and Marie Kelly joined forces for a 68-run stand.
Kelly was dismissed five short of her half-century and when Jones went for 49, Spirit were 4-124 with 28 runs required off 22 balls.
The equation was whittled down to 12 off nine balls, but Carey produced a tight five-ball spell before Matthews dismissed Nadine de Klerk and conceded only three runs from the final three balls to ensure Spirit ended on 5-151.
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