Left-hander Jadeja top-scored with 43 off 26 balls to guide Chennai to 167-9 after being invited to bat first in Punjab's adopted home ground of Dharamsala.
Jadeja then returned figures of 3-20 from his four overs of left-arm spin to help restrict Punjab to 139-9 for Chennai's sixth win in 11 matches as they climbed to third in the table.
The top four teams will make the play-offs with the final on May 26 in Chennai.
The performance from the veteran Jadeja comes as a welcome sign ahead of the T20 World Cup in June in the West Indies and the United States.
Chennai suffered an early blow with Sri Lanka pace bowler Matheesha Pathirana set to return home due to a hamstring injury.
Pathirana, called "Baby Malinga" for his slinging action modelled on former Sri Lanka quick Lasith Malinga, was Chennai's standout bowler and took 13 wickets in six matches.
But medium-pace bowler Tushar Deshpande took on the responsiblity in the absence of Pathirana and injured Deepak Chahar as he struck twice in his first over and Punjab's second in the chase.
Deshpande sent Jonny Bairstow, bowled for seven, and then Rilee Rossouw, bowled for a duck, trudging back to the pavilion in the space of four balls.
Prabhsimran Singh, who made 30, and Shahshank Singh, who hit 27, attempted to rebuild in their stand of 53 but their departure triggered a collapse.
Jadeja struck regular blows including skipper Sam Curran to rattle the middle-order and derail the opposition chase.
Earlier Chennai suffered from a lack of partnerships despite a second-wicket stand between skipper Ruturaj Gaikwad, who hit 32, and Daryl Mitchell, who struck 30.
Jadeja took charge and with some help from the middle order as he took Chennai to a par total at the picturesque ground overlooking the Himalayas.
But the Sunday crowd were left disappointed when veteran M.S. Dhoni was bowled for a first ball duck off a slower ball from Harshal Patel, who along with Rahul Chahal took three wickets each.
Jadeja smashed three fours and two sixes before departing in the 20th over from left-arm quick Arshdeep Singh.
