Marsh, who has had many downs in his international career to date, stepped up and finished 126 not out for the hosts, who declared on 442-8 in their first innings.
In reply, England got to 29-1 in their first innings before rain brought an early end to the second day, with the visitors still 413 runs behind the hosts massive score.
Broad got England off to a great start before Paine and Marsh put on a great partnership
Day two at Adelaide started with the hosts on 209-4 with Peter Handscomb 36 not out and Marsh 20 not out.
The pair would have wanted to push the score on but the visitors weren't having any of it as Stuart Broad removed Handscomb with the third ball of he day for 36.
The early wicket brought Tim Paine to the crease under pressure to make a score. The wicketkeeper showed his intent straight away and alongside Marsh the pair took their partnership past the fifty mark.
Paine's brave shot making also got its reward as he passed his own half century before he was removed for 57 by Craig Overton.
The Aussies lost no further wickets in the first session as they ended on 306-6 with Marsh 49 not out and Micthell Starc four not out.
Cummins provided Marsh with great support as the Aussie number six brought up his fifth test century
After tea, it didn't take long for Marsh get to his own half-century as he looked like he wanted to keep going.
Starc though after staying at the crease for a while was removed by Broad for six to leave the score on 311-7.
Pat Cummins came to the crease to join Marsh at the fall of the Starc wicket and after taking a long time to get off the mark, he also showed his intent to push the score forward.
Cummins and Marsh frustrated the visitors as they took their partnership passed the half-century mark as Marsh also brought up his fifth test century in the process.
Therefore, at the end of the second session, the Aussies finished on 409-7 with Marsh unbeaten on 103 and Cummins 44 not out.
The Aussies declared on 442-8 in the final session
After dinner, Cummins was dismissed for 44 by Overton in the first over at the break but after that the Aussies went all out attack.
Nathan Lyon, alongside, Marsh started playing their big shots as Steve Smith finally declared the Aussie innings with the score on 442-8 to put some pressure on the visitors opening pair before the end of play.
Stoneman fell early but rain brought an early end to day two
Alastair Cook and Mark Stoneman, therefore, began the England response in solid fashion as they both played their shots before Stoneman was trapped LBW by Starc for 18.
Not long after though the heavy rain came at Adelaide and that brought an end to the day's play early with the visitors on 29-1, still 413 runs behind the Aussies and in need of a good batting performance on day three to get themselves back into the game.