Australia were bowled out for 137 runs in their second innings, setting a target of 106 runs for India on the third day of the fourth and final cricket Test against here on Monday.
Earlier, India were bowled out for 332 at lunch, taking a crucial 32- run lead in their first innings.
Cummins bowled a wide length ball which Jadeja tried to drive without using his feet and guided a thick inside edge onto the stumps.
Incoming batsmen Bhuvneshwar Kumar departed in the next over without disturbing the score. He was sent packing by left-arm spinner Steve O'Keefe.
O'Keefe, who took the wicket in his first over of the day, tossed the ball and Kumar drove on the up and away from the body to give a simple catch to skipper Steve Smith.
Saha, who seemed good at the crease was the next one to go. He was dismissed by Cummins when the scoreboard was reading 318/9. His 102-ball knock was laced with only two boundaries.
Tailenders Umesh Yadav (2 not out) and debutant Kuldeep Yadav (7), however, added 14 runs for the last wicket to frustrate Australian bowlers and helped India to get past 330-run mark.
For Australia spinner Nathon Lyon scalped five wickets while Cummins took three wickets. Josh Hazlewood and O'Keefe chipped in with one wicket each.
India (First Innings): 332/10 (Ravindra Jadeja 63 Lokesh Rahul 60, Cheteshwar Pujara 57 batting; Nathon Lyon 5/93, Pat Cummins 3/94) vs Australia (First Innings): 300.