Reddy, Sundar lead India fightback to 326-7 against Australia
In overcast conditions at the Melbourne Cricket Ground, Reddy posted a maiden Test half-century and was 85 not out before light rain caused tea to be called 15 minutes early.
Sundar was equally defiant on 40 off 115 balls in an unbroken eighth-wicket stand of 105 to leave India still trailing by 148 runs.
The pair batted through the second session in largely untroubled fashion, passing the follow-on mark and seeing off the second new ball to frustrate the home side, who have been in the driving seat since posting 474 in their first innings.
They held up Australia's push for a win that would put them 2-1 up going into the fifth and final Test in Sydney next week.
Batting at number eight in an Indian line-up that has largely struggled for runs, Reddy has been a shining light in his debut series.
The 21-year-old's 264 runs have come at an average of 66, although he had fallen narrowly short of 50 on several occasions.
He mixed resolute defence with some classical straight-bat stroke play in facing 119 balls, scoring eight fours and a six -- the eighth time he has cleared the ropes this series.
Sundar, who missed the second and third Tests, was recalled primarily for his off-spin.
The 25-year-old survived a freakish chance when he was on 18.
Attempting to flick a leg-sided delivery from Mitchell Starc, the ball flew from the back of the bat into the slip cordon where a diving Steve Smith spilled a one-handed opportunity.
India lost Rishabh Pant and Ravindra Jadeja in the first session, advancing from 164-5 overnight to 244-7 at lunch.
Seamer Scott Boland, who taken 3-49, removed the aggressive Pant for 28 off 37 balls before off-spinner Nathan Lyon accounted for Jadeja for 17.
Pant's slightly streaky knock ended when he over-balanced while attempting a ramp shot for six, top-edging the ball to third man where Lyon held the catch.
Jadeja batted more doggedly, taking 18 balls to score his first runs of the day, before playing back to a Lyon delivery that skidded on and trapped him lbw.
The forecast for the remainder of the afternoon was for sporadic showers.