Wicketkeeper Paine, who was stunningly recalled to the Australian team for the first time in seven years, led the way with a swashbuckling 57 off 102 balls.
Paine, who took a couple of painful blows on his right index finger which he seriously fractured seven years ago, shared an 85-run stand with Marsh before he was caught on the boundary pulling Craig Overton.
Paine had eight pins and a metal plate inserted into the shattered finger which caused him to originally lose his spot in the Test side back in 2010.
Paine raised his third Test fifty off 91 balls with a big six off Moeen Ali over wide long-on and then a two off Stuart Broad.
Marsh, in his eighth recall to the Australian team, neared another half-century following his 51 in Brisbane as the Australians passed 300 after being sent into bat in the first-ever Ashes day-night Test.
At tea, the home side were 306 for six, a score considered above par for a pink ball Test at Adelaide Oval with Marsh on 49 and Mitchell Starc on four.
Australia have won the three day-night Tests they have played at home, against New Zealand (2015), South Africa and Pakistan (both 2016).
The average first-innings score in these games is 297, which drops to 231 in the two Tests at Adelaide Oval.
Marsh had an lbw decision on 29 by James Anderson overturned when a review showed the ball would have gone over the stumps.
Anderson was frustrated again, much to the delight of the home crowd, when a review denied him again after Paine on 24 had been given out lbw on the field.
Peter Handscomb only lasted three balls before he was trapped leg before wicket playing back on his overnight score of 36 by fired-up Stuart Broad.
Broad gave Handscomb an animated send-off as the tourists looked to regain lost initiative from the opening day after sending Australia into bat.
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