The experienced left-hander, in his eighth recall to the Australian team, put together his fifth century in his 25th Test, an unconquered 126 off 231 balls which lifted the home side to 442 for eight declared.
When rain brought an early finish to day two, the tourists were 29 for one and trailing the Australians by 413 runs with three days remaining.
Marsh, along with wicketkeeper Tim Paine, were the major surprises in the Australian team for the opening Ashes Tests. But the 34-year-old batsman has staked his claim for retention with another solid innings at number six.
He backed up his 51 in Brisbane to bring his series tally to 177 runs and strengthen Australia’s middle order.
“There’s a lot of relief there. I’m just really happy,” Marsh said.
“I haven’t thought about all the incidental noise (criticism) and my selection for the team.
“I’ve just tried to come in and feel nice and relaxed. I’ve felt good about my game the last three or four months.”
Of the criticism before the series about his selection, Marsh added: “I didn’t read a thing. I knew there was some extra noise but I just stayed away and focused on preparing well.
“Six months ago I wasn’t sure whether I’d be back here. I’d always dreamt of getting back in.”
Marsh was the bulwark of the Australian innings, hitting 15 fours and a towering six off Stuart Broad in his first Ashes Test hundred.
“We got a message just before tea that Smithy (skipper Steve Smith) wanted to up the ante a bit and gave us free range,” he said of his late lusty hitting ahead of the declaration.
Marsh had a nervous few moments after seeking a review when he was given out leg before wicket on 29 to James Anderson.
But the decision was overturned when the review projected that the ball would have gone over the stumps.
“I probably thought it was outside leg more than going over,” Marsh recalled.
“When I saw the ball pitch in line I thought I might have been in a bit of trouble.”
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