The pair shared in a partnership of 301.
Marsh, who was unbeaten on 100 at tea, strode out to the crease during the morning session after his older brother, Shaun, had departed for 28.
The 26-year-old made a nervous start and some of his flighty shots only narrowly went wide of fielders.
He was also lucky that his inside edge off the bowling of James Anderson missed his stumps.
But Marsh slowly worked his way into the contest, with his cover drive off Stuart Broad the pick of his early shots as his score moved to 18.
Marsh started racking up the boundaries, bringing up his half-century midway through day three.
His confidence continued to grow, and his shots reflected his mood.
Shortly before tea, Smith and Marsh took Australia's score past England's first-innings total of 403.
The pair's stand had grown to 154 by that stage, and England looked bereft of answers.
Marsh started the domestic season as a batsman, cracking scores of 124, 67 not out and 80 not out during the one-day competition, and producing Sheffield Shield scores of 95 and 141.
He only returned to bowling duties in late November, putting doubt as to whether he was ready for test action. Selectors opted to pick Marsh for the third test in the fear the Waca deck could end up becoming a batsman's paradise.
Marsh returned figures of 0-43 off nine overs.