Chasing 131 for victory in a match that was reduced to 26 overs a side, Marsh scored 46 not out as the home side cruised to an easy win to take a 1-0 lead in the three-match series.
Matt Renshaw was unbeaten on 21 alongside Marsh as Australia reached 131-3 with 29 balls remaining. Josh Philippe contributed 37, batting at number four.
"Obviously the weather played its part today," Marsh said. "But it's nice to get a win.
"The ball was swinging around for both teams out there so it was a little bit of a challenge to get through.
"I was proud of the way our young guys came out and got the job done."
Marsh, who was also named player of the match, won the toss and chose to field due to the inclement weather around the Western Australia city.
It paid dividends as India's innings was hampered by rain delays, which frustrated the visitors who struggled to build any momentum.
A quickfire 38 off 31 balls from KL Rahul helped India to recover to 136-9, with Australia set 131 to win after the total was adjusted on the Duckworth-Lewis-Stern system.
Australia's opening bowlers Josh Hazlewood and Mitchell Starc troubled the Indian batsmen with a good line and movement.
Hazlewood had Rohit Sharma caught at second slip for eight before Starc claimed Virat Kohli without scoring, leaving the visitors 21-2.
India skipper Shubman Gill was caught by wicketkeeper Philippe off Nathan Ellis for 10 before the first rain delay, with India 23-3 after 8.5 overs.
"When you lose three wickets in the powerplay you are always trying to play a catch-up game," Gill said.
"But there are a lot of learnings for us from this game and a lot of positives as well."
Hazlewood grabbed his second victim when Shreyas Iyer gloved a ball to Philippe before another long delay with India at 45-4.
When they eventually resumed, the game was reduced to 26 overs.
Rahul smashed two huge sixes but fell on the boundary going for a third.
Nitish Reddy blasted 19 runs off the last two overs but the reduced total was never enough.
The two teams meet again in Adelaide on Thursday before the final match at the Sydney Cricket Ground on Saturday.
