Riding on Naman's scintillating unbeaten 219 and three-wicket burst from Jasprit Bumrah (3/42), India A took a commanding position over the hosts at the Allan Border Field.
Resuming at his overnight score of 82, Naman added 122 runs with No. 10 and 11 batsmen, whose combined contributions in those two partnerships was 11 runs, before India A declared their innings at 475 for nine 130 overs.
Starting the day on 304 for six, Naman single-handedly guided India A forward and reached his century in the 10th over of the morning, with a six off leg-spinner Cameron Boyce.
With wickets tumbling from the other end, Naman adopted an attacking approach and scored a flurry of boundaries, including a four and two sixes in successive deliveries off Boyce, to move to 152 and take India A's total to 400, before Moises Henriques had his namesake Pragyan Ojha caught behind. Pragyan's contributed only fours runs in the 47-run ninth-wicket partnership.
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Naman was merciless in his approach as he dominated another partnership with a lower-order batsman Jasprit Bumrah, adding 75 runs in the next 91 balls to declare India A's innings on 475 for nine.
Naman reached his 200 with another six, this time off fast bowler Chadd Sayers. His knock came off 250 balls with the help of 29 fours and eight sixes.
In reply, Phil Hughes and Alex Doolan put on 33 for the first wicket before Bumrah struck in the ninth over to remove Doolan.
Peter Forrest then added another 33 with Hughes before Bumrah struck again.
Hughes fell at the same score, bowled by Dhawal Kulkarni, before Pragyan Ojha and Umesh Yadav joined the party to leave Australia A reeling at 99 for six.