Cheteshwar Pujara, after getting out for a duck in the first innings in his 100th Test, championed India's chase of 115, scoring 31 runs off 74 balls on a difficult Delhi wicket.
The Australian batters paid the price for some atrocious shot selection as Jadeja, who enjoyed a 10-wicket match haul, along with Ravichandran Ashwin (3/59) decimated the visitors in the morning session, bowling them out for 113 in 31.1 overs. The last nine wickets fell for 52 runs.
KL Rahul (1) cut a sorry figure, but Indian batters showed how to play spin as the target of 115 was completed in 26.4 overs.
Cheteshwar Pujara had something to cheer about on his 100th Test appearance as he remained unbeaten on 31 and fittingly hit the winning boundary. India have now put one foot in the final of the World Test Championship in England in June, having taken an unassailable 2-0 lead in the four-match series.
The win was India's 100th against Australia across formats. The third Test will be played in Indore from March 1.
Starting the day at 61 for 1, Jadeja's arm balls became a lethal weapon with as many as five Australian batters getting out trying to play sweep shots of deliveries that kept low on a typical third day Ferozshah Kotla track.
Australia lost nine wickets for only 52 runs and it was not the pitch, but the fear of the unknown that led to their eventual downfall.
Steve Smith, Matt Renshaw, Alex Carry, Pat Cummins and Matt Kuhnemann were all guilty of playing the ugly slog sweep and some tried non-existent reverse sweep off deliveries bowled on either middle or leg stump line.
They were either bowled or adjudged leg before in the process as the deliveries started keeping low.
Ashwin also played the supporting act to perfection as eight Australian batters failed to reach double figures save the overnight pair of Travis Head (45) and Marnus Labschagne (35), who had briefly counter-attacked last evening with some degree of success.
But it all changed in the morning session once Head got an off-break from Ashwin and the edge was picked up by Kona Bharat behind the stumps.
It is a cardinal mistake to play a sweep or reverse sweep off straighter ones or sliders if there isn’t enough bounce. The ball that trapped Steve Smith plumb in front was on leg-middle and it was a fair call.
The ideal technique of playing on tracks where the ball starts keeping low is to plonk the front foot forward and play with a straight bat. When a player stretches the front foot forward, the chances of silly point or short leg being in business also reduce.
Instead, if you are on the back foot or trying to play across the line shots like sweep and reverse, there is every possibility that spinners will mostly keep it in line of stumps waiting for either bowled or leg before decision.
Labuschagne, who looked confident until then, went on backfoot to a delivery that was supposed to be met on the front foot with a big stride. The result was the ball kept low and the batter was castled.
Matt Renshaw doesn’t have the technique or wherewithal to guts it out on these Indian dustbowls and he has been a ‘walking wicket’ for the home team.
Having replaced a concussed David Warner, Renshaw went for a sweep off Ashwin when the ball kept really low and the shot was not on.
The only delivery that was a classic left-arm orthodox one was bowled to Peter Handscomb (0), the best batter in the first innings. Jadeja, for a change, tossed it up and drew him forward before it turned away enough to get an outside edge into Virat Kohli’s hands.
Pat Cummins’s ugly slog sweep shot was more out of anger and frustration rather than purpose and Matt Kuhnemann, while giving Jadeja his seventh wicket, looked as clueless as possible.
Rohit showed how to play spinners on low bounce track.
When India started the chase, their skipper Rohit Sharma (31 off 20 balls) showed how to tackle the Australian spinners before being run out due to a mix-up.
Unlike Labuschagne, who preferred to stay on back foot even to flighted deliveries, the moment Rohit saw the ball being given air, he would put a big stride forward and lift it in the arc between sight screen and cow corner.
Rohit’s stay was short and sweet one, but certainly a lesson in playing spinners.