Warner smashed five fours and three sixes in his 34-ball 49, while all but three of Marsh's 23 off 12 balls were fours, but their teammates could not maintain the momentum on Thursday as they chased Rajasthan's 5-185.
Rajasthan's second straight victory continued the early trend of home teams dominating in the lucrative T20 league. Visiting teams have lost all nine games this season.
Rajasthan and Chennai Super Kings are the only two teams with two wins from two matches, with the second round of games almost complete.
Parag, who smashed six sixes and seven boundaries, anchored Rajasthan after Rishabh Pant won the toss in his 100th IPL game and elected to field.
Delhi struggled against spinner Yuzvendra Chahal (2-19) in the middle overs before being restricted to 5-173, despite Tristan Stubbs (44 not out) counterattacking in the death overs.
Rajasthan ran into early trouble inside the batting power play when Yashasvi Jaiswal was clean bowled by Mukesh Kumar and Jos Buttler was out lbw attempting a reverse sweep against wrist-spinner Kuldeep Yadav.
Fast bowler Khaleel Ahmed then reduced Rajasthan to 3-36 when he had skipper Sanju Samson caught behind in the eighth over before Ravichandran Ashwin, promoted to No.5, revived the innings with a cameo of 29 off 19 balls with Parag.
Parag then took charge against Delhi's pace bowler Anrich Nortje (1-48) and Kumar (1-49) as Rajasthan plundered 77 runs in the last five overs.
Mitch Marsh goes on the attack during his 12-ball cameo for Delhi Capitals. (AP PHOTO)
Parag hammered South African Nortje for 25 runs in the last over that included three fours and two sixes while Kumar conceded 30 off his last two overs.
Australians Warner (49) and Marsh (23) got Delhi off to a rollicking start, Marsh smashing five boundaries before Nandre Burger's twin strikes pulled things back for Rajasthan.
Burger clean bowled Marsh with a pacy swinging delivery before Ricky Bhui couldn't get out of the way of a quick bouncer that brushed his gloves and Samson took a straightforward catch behind the wickets.
Sharma then held onto a spectacular catch at short third man to deny Warner a half-century while Pant showed brief signs of aggression before edging Chahal to Samson.
With 61 needed off the final four overs, Stubbs smashed three sixes and two boundaries, but Avesh bowled a brilliant last over for only four runs.
