Marsh notched his fifth Test century for the Baggy Greens with an unbeaten 125 as the hosts posted a daunting total in a rain-affected second day.
Australia negotiated their way to 209-4 on the first day and frustrated the tourists with some disciplined batting, despite losing Peter Handscomb with the third ball of the day.
Marsh was ably supported by a half-century from Tim Paine before putting on an eighth-wicket stand of 99 with Pat Cummins as the hosts declared on 442-8 after dinner.
Australia still had time to take an early wicket as Mitchell Starc trapped England opener Mark Stoneman lbw for 18 before rain brought an early end to proceedings to the second day.
“It is an amazing feeling to bring up a hundred in an Ashes Test match, there was a lot of emotion there,” said Marsh. “I really enjoyed today. I’m just really happy, to have my family here as well and witness it was pretty special. I’ve just enjoyed my cricket over the last little period and I just got to keep it going.
“It was a good day for us. I thought the way Painey and Paddy (Cummins) came in and batted and to get us over the 400-mark, it was a good day for us.
“It would have been nice to get all the overs in tonight but hopefully we can come out tomorrow morning and take a few early wickets and put them under pressure.
“The way Paine came out and the intent he showed was awesome and obviously Paddy did a job up in Brisbane and has done the job again today with the bat so I thought those two were really good.
“We got a message from Smithy (captain Steve Smith) to up the ante just before tea and have a crack after tea. It’s disappointing with the rain but that’s the way it goes and hopefully we can come here tomorrow morning and get an early breakthrough.”
England head coach Trevor Bayliss remains optimistic of picking up a result to keep the tourists’ Ashes hopes alive and he also defended captain Joe Root’s decision to bowl first in the second Test.
Bayliss said: “I was very happy with his decision, it is a well-documented fact now that we struggle to take wickets on flat ones (pitches) and Joe wanted to give our bowlers the best opportunity to take 20 wickets in the match.
“Before the first rain break, I thought we bowled pretty short but we came out after that and thought we bowled pretty well. We went past the bat a lot, but that’s the game.
“Another day, with an extra couple of nicks, it could have been a completely different story, but that’s gone and we have to concentrate on our batting tomorrow.
“It’s not nice to bat under the lights, so I guess it is a bit of a bonus there for us. We look forward to tomorrow and hopefully batting big.
“It’s another full day tomorrow and hopefully (we can get) some big runs, with two days to go, there is plenty of time for a result.
“Look, 440-odd is not a huge score here in Australia on good wickets and hopefully this one flattens out as it goes on. I’m sure they will come out tomorrow and make a good account of themselves.”