To the roar of a large contingent of Indian supporters at the Melbourne Cricket Ground, seam bowling all-rounder Reddy reached three figures in the final session on day three.
The 21-year-old all-rounder was on 103 not out, with India 354-9 in response to Australia's 474.
Reddy took 172 balls to reach the milestone, hitting 10 fours and one six.
He lifted Scott Boland over mid-on for four to bring up three figures, having earlier flashed a cover drive off Mitchell Starc to the boundary to reach 50 for the first time.
A 127-run stand with Washington Sundar fell three runs short of surpassing the record for India's highest eighth-wicket partnership on Australian soil.
Reddy was the aggressor as he continued the fine batting form that has marked his debut series.
In his first six Test innings, he has scored 282 runs at an average of just over 70.
