Australia T20 captain Marsh hit eight boundaries, including three sixes, in a 34-ball 50 as he shared an opening partnership of 89 with Ryan Rickelton at Headingley.
South African Rickelton made 40 off 22 deliveries for the second-placed Sunrisers, while Harry Brook, captain Zak Crawley and Dan Lawrence contributed 23, 34 and 29 respectively in a total of 4-201.
Australian Opener Matthew Short top-scored for Fire with 43 before being caught by Brook as Carse, who finished with figures of 3-24, claimed his second wicket after removing Phil Salt for 13.
England mainstay Joe Root added 31 from 22 balls but the visitors fell well short, finishing on 6-130 as their hopes of a top-three finish suffered a major setback.
In the women's section, another Australia star Phoebe Litchfield hit a half-century as Sunrisers Leeds kept alive their semi-final hopes with a comfortable six-wicket win which eliminated Welsh Fire.
In a must-win game for both sides, Fire were fortunate to reach 8-121 after being put into bat at Headingley as top scorer Freya Kemp was dropped three times during an unbeaten 72 off 45 balls.
Australia's Annabel Sutherland fumbled a straightforward catch at mid-off to reprieve Kemp on just six and later squandered another major opportunity at long-off.
Sunrisers all-rounder Deepti Sharma took 3-13 and would have claimed four wickets had Kemp not been dropped again on 62, this time by Cassidy McCarthy at deep cover.
The chase got off to a bad start when Bryony Smith was dismissed for a duck from the third ball, before Litchfield contributed 55 off 25 deliveries, including six fours and three sixes.
Sutherland partly redeemed her poor performance in the field with 28 off 18 before a four from Jess Jonassen secured victory with 26 balls remaining.
