The tourists may have feared a stumble at the first hurdle under lights after Marsh (126 not out), Tim Paine (57) and Pat Cummins helped Australia rack up 442 for eight declared.
Instead, in 9.1 overs before evening rain brought day two to a premature end, they lost only Mark Stoneman - lbw to a full ball from Mitchell Starc - in a stumps total of 29 for one.
England captain Joe Root’s gamble to bowl first here brought only aggravation and his team nonetheless remains badly up against it to somehow remain only 1-0 down.
Australia bagged a remarkable 200 for three in the first two sessions, despite losing Peter Handscomb to the third ball of the day.
When Stuart Broad pinned him deep in his crease lbw, England’s hopes briefly rose at 209 for five.
Then for a few tantalising seconds not long afterwards, they thought it was 240 for six when Chris Gaffaney gave what appeared at first sight a very feasible lbw against Marsh, who got in a rare tangle pushing forward to James Anderson.
He rightly chanced a review - almost certainly in the hope the ball had pitched outside leg - only to discover instead that technology projected it going on to clear middle stump.
Marsh therefore survived on 29, and in similar circumstances so did Paine on 24 in the luckless Anderson’s next over.
England were still threatening to take a clutch of wickets, bowling better than on Saturday on a pitch providing more lateral movement, yet they mustered just one more before tea when Paine mis-pulled Craig Overton to deep square leg.
That ended a crucial stand of 85, followed by one of even more substance as Marsh was joined by Cummins - surely one of the best number nines in this or any era.
England did not make it easy, and Cummins needed significant skill and self-belief as he took 37 balls to get off the mark.
He eventually did so with a tucked-up, aerial cut for four off Overton - after which he and Australia never looked back.
Marsh had his near five-and-a-half-hour century in safe keeping by dinner when a pinpoint pull off Chris Woakes brought him his 12th four from the 213th ball he faced and took Australia past 400.
There was still time for the last ball before the break to serve up a tragi-comic moment as apt summary of England’s fortunes when Marsh spliced a short ball from Woakes gently behind square on the off-side only for James Vince and Alastair Cook to collide with one another rather than either take the catch.
In four further overs, after Cummins upper-cut to third-man to fall short of a maiden Test 50, there was some crowd-pleasing slapstick hitting from Nathan Lyon and a memorable six from Marsh over long-on off Broad - a mighty and memorable strike.
By then, dating back to last week’s second innings in Brisbane, England had spent 199 overs in the field since they last had a bat.
In those circumstances, they did not fare as badly as many feared in a mercifully truncated session.