The Australian hit six sixes and nine fours as Delhi stopped Punjab at 202-6 after scoring 231-4 - the highest total of this year's tournament - for their second victory in five matches.
Punjab's hopes of achieving a stiff target in the tall-scoring game receded after the dismissal of Marsh, caught by skipper Virender Sehwag off South African paceman Morne Morkel in the 18th over.
Marsh added 72 for the second wicket with skipper Adam Gilchrist, who hit four successive fours off seamer Ajit Agarkar during his 33-ball 42. It was Punjab's second defeat in five games of the Twenty20 tournament.
Delhi were earlier indebted to Australian David Warner and Sehwag for setting a challenging target, with each scoring 77.
Sehwag, without a half-century in the previous four games, returned to form with a 35-ball knock which contained four sixes and eight fours while Warner hit seven boundaries and four sixes in his 48-ball knock.
Hosts Delhi made a spectacular start as Sehwag and Warner plundered 146 off 11.4 overs, much to the delight of a sizeable crowd at the Ferozeshah Kotla ground. It was the highest opening-wicket stand of the ongoing tournament.
Sehwag once punished Australian spinner David Hussey, hitting three successive sixes before being caught in the deep while attempting another big shot off the next delivery.
Warner matched his partner shot for shot, reaching his half-century with a six over mid-wicket off seamer Paul Valthaty. Venugopal Rao then helped Delhi cross the 200-mark with a 15-ball 28 not out.
Delhi Daredevils 231-4 in 20 overs (V. Sehwag 77, D. Warner 77. V. Rao 28 not out) beat Kings XI Punjab 202-6 in 20 overs (S. Marsh 95, A. Gilchrist 42, D. Hussey 20; A. Agarkar 2-48) by 29 runs.