The 21-year-old sent Indian fans into delirium as he strode forward to thump Scott Boland over mid-on for four to raise his hundred late in the day, bringing tears to the eyes of his overjoyed father in the Melbourne Cricket Ground crowd.
Reddy strode off unbeaten on 105 when bad light and rain brought stumps an hour early, with India 358 for nine, still trailing Australia’s first innings 474 by 116 runs.
Tailender Mohammed Siraj was two not out but enjoyed one of the day’s biggest cheers when he blocked out Australia’s paceman-captain Pat Cummins for three balls.
That allowed righthander Reddy, stranded at the non-striker’s end on 99, to complete his ton in the next over.
Playing in his fourth test, Reddy planted his bat in the turf, put his helmet over the handle and saluted the sky as a huge crowd of 83,073 gave him a standing ovation.
The MCG fans have now seen two young stars rise this test, with Australia’s 19-year-old opener Sam Konstas producing a thrilling knock of 60 on day one of his debut.
India’s 25-year-old number eight Washington Sundar also produced an important 50 as he and Reddy combined for a 127-run partnership and defied the Australia’s bowlers for more than a session.
Nathan Lyon broke the partnership by having Sundar edge to Steve Smith at slip before Jasprit Bumrah fell for a duck, edging Cummins to Usman Khawaja in the slips.
Australia developed an injury concern before tea, with paceman Mitchell Starc pinching at his back with an apparent muscle strain.
A team physio attended to Starc as he fielded in the deep.
India had resumed on 244 for seven after lunch, still 31 runs short of avoiding the follow-on, after wicketkeeper Rishabh Pant holed out for 28 with a poor reverse scoop in the morning.
Nathan Lyon then broke a 30-run partnership between Reddy and all-rounder Ravindra Jadeja by dismissing the latter lbw for 17.
Sundar was dropped on 18 early in the middle session when he attempted a leg-side glance that sent an inside edge flying behind the wicket.
Smith lunged across from second slip but grassed the one-handed chance.
Reddy brought up his first test fifty in style with a lofted square drive which despatched a loose Starc delivery to the ropes for four.
He later brought up the 100-partnership with Sundar with a sumptuous cover drive. It was made all the more sweet for Indian fans in a huge day three crowd when Lyon stumbled at the boundary to concede a four.
While his senior teammates fell by the way-side, Reddy continued to impress in his debut test series.
His sound technique and composure in the lower order was a relief for Indian fans following his teammates’ shaky start in the morning.
The five-test series is level at 1-1, with the final match to come in Sydney.