Marsh cracked 65 from 39 balls, with one of his four sixes making a dent in the sponsor's car beyond the boundary. But after his departure LSG, who are coached by Justin Langer, lost momentum to close on 7-205.
That proved far from enough, even with Sunrisers missing Covid-hit Travis Head, who spent the night in quarantine in his hotel room after flying in from Australia.
With contributions throughout the order, topped by a 20-ball 59 from Abhishek Sharma, the visitors passed the target with six wickets and ten balls to spare.
"The win gives us a lot of confidence going into next year," said Cummins, 'it shows when we get it right we're a really good side."
The Australian captain had not been so chilled after bowling the first ball of the match and watching Marsh lift it over the covers for four, then pulling the fourth from outside off to over the ropes at deep midwicket.
The West Australian took 15 off the eight balls he faced from Cummins and was almost as harsh on everyone else, reaching a chanceless 50 off 28 balls. He was dropped on 57 - a tough chance - before being caught at short third to give left-arm spinner Harsh Dubey his maiden IPL wicket.
That left LSG 1-115 in the 11th over, the perfect platform to go well beyond 200. But after Aiden Markram (61 off 38) also went Sunrisers squeezed the rate, with Rishabh Pant's poor form continuing, the home skipper making seven off six balls.
However, a late flourish in which Nicolas Pooran made 45 off 26, enabled LSG to at least pass 200. Cummins ended with 0-34 off his four overs
Judging an innings has been difficult at Ekana, but despite Will O'Rourke dismissing Atharva Taide (13) early on it soon became clear LSG did not have enough.
Sunrisers took 72 off the six-over powerplay and passed 100 in the eighth over, for two wickets down. By the time the strategic timeout was taken 27 were needed in four overs, a formality with seven wickets left.
The result leaves Mumbai Indians and Mitch Starc's Delhi Capitals left to contest the final play-off place with Gujarat Titans, Josh Hazlewood's Royal Challengers Bengaluru and Ricky Ponting's Punjab Kings already qualified.
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