Resuming at 238/5 post lunch, New Zealand were bundled out for 262, losing their last five wickets in a space of 20 minutes, out of which three came in one over from Jadeja.
Ravichandran Ashwin, who removed Tom Latham and Kane Williamson early in the day, finished with four wickets as nine of the visitors' wickets fell to spinners.
India later finished Day 3 in control of proceedings, with a total 159/1 on board at stumps, and Murali Vijay and Cheteshwar Pujara unbeaten with scores of 64 and 50, respectively.
Both Ashwin and Jadeja have been instrumental in India's success at home in past few years. It will not be be an exaggeration to say both were the deciding factors of India's success in the home series against South Africa last year.
Virat Kohli's team not only won the series 3-0 but but also displaced the Proteas as the top-ranked Test team. The margin of those victories at Mohali (108 runs), Delhi (337 runs) and Nagpur (124 runs) were also impressive.
Ashwin and Jadeja shared 54 wickets between them in the series, which amounted to 78 percent of the wickets taken by all Indian bowlers. Even during the home series against Australia in 2012-13, the duo grabbed 53 of the 79 scalps as the hosts won 4-0.
Even after the win against South Africa, Ravi Shastri, former Team India Director, said both Ashwin and Jadeja complement each other very well.
Ashwin is 30 while Jadeja is even younger (27). If both of them can continue to stay fit, India can expect better days ahead.