Half-centuries from Marsh and Englishman Dan Lawrence set Sunrisers Leeds on course for a five-run win over Southern Brave in the men's Hundred at Headingley.
Opener Marsh smashed six sixes and four fours in a knock of 69 off 34 balls before Lawrence's unbeaten 51 from 25 balls took the hosts to 5/187.
Sunrisers captain Zak Crawley was dismissed for a golden duck as England spinner Adil Rashid claimed his third wicket of the afternoon after earlier removing Marsh and fellow opener Ryan Rickelton (37).
Harry Brook was then clean bowled for three by Aussie allrounder Marcus Stoinis before Lawrence's efforts and a rapid 21 from Tom Alsop helped the Sunrisers finish strongly.
Ben McKinney led Brave's response with 44 from 23 deliveries, while fellow opener Jamie Smith hit 30 from 18 and Stoinis plundered 31 from 16.
Tristan Stubbs kept the visitors in contention with an unbeaten 43 from 20 balls. But the home team held on for a first victory of this year's tournament, while Brave remain winless after two matches.
In the women's Hundred at Sophia Gardens, New Zealand's Sophie Devine and Australia's Georgia Wareham headlined a powerful display from Welsh Fire to sweep aside MI London by 60 runs.
Fire were beaten by Southern Brave in their opener but bounced back by posting 4/177 – the third highest total in the tournament's history.
Captain Devine made 52 from 29 balls and Wareham 43 from 20 after openers Georgia Voll and Ella McCaughan contributed 42 and 27 respectively.
Grace Potts then claimed three wickets for 24 as MI London crumbled to 117 all out to suffer their second successive defeat.
Also on Saturday (Sunday AEST), Southern Brave made it two wins from two with a five-wicket success over Sunrisers Leeds.
Jemimah Rodrigues made an unbeaten 42 from 34 deliveries, while Australian captain Sophie Molineux chipped in with 21 from 17 as the visitors chased down 117 with four balls to spare.
Bryony Smith's 34-ball 48, which included six fours and a six, underpinned the Sunrisers' total of 116.
Elsewhere, Rachin Ravindra registered the joint fourth-highest score in the history of The Hundred men's competition to propel Welsh Fire to a 15-run victory over MI London.
Ravindra whacked seven fours and seven sixes in a 44-ball 98 as he shared a match-winning partnership of 116 with Joe Root in Cardiff.
Root contributed 29 from 26 deliveries after Fire lost openers Phil Salt and Matt Short early and struggled to 25 for two at the end of the powerplay.
With a century in sight, New Zealander Ravindra was eventually caught by Jason Roy off the bowling of Trent Boult with two balls remaining before the hosts reached 5/167.
The Fire then maintained their winning start by restricting their opponents to 6/152.
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