Left-handed opener Dhawan, who hit one six and 14 fours in his 57-ball knock, put on 131 for the opening wicket with Ravi Teja (60) as Deccan made 198-2 before bowling Punjab out for 116.
Skipper top-scored with a 37-ball 51 for Punjab, who put in a below-par batting and fielding performance. The captain, who hit two sixes and six fours, added 61 for the third wicket with Karthik (11).
Deccan virtually wrapped up the match when Australian paceman Daniel Christian dismissed Gilchrist and Karthik in the space of three balls to reduce Punjab to 84-4 in 11 overs.
Leg-spinner Mishra's hat-trick came in his third over when he removed Ryan McLaren, Mandeep Singh and to eventually finish with 4-9.
Chennai (18 points), Bangalore (17), Kolkata (16) and Mumbai (16) have now qualified for the play-offs. They are followed by Punjab (14), Rajasthan (13), Deccan (12), Kochi (12), Pune (eight) and Delhi (eight).
Deccan, who finished with six wins in 14 matches, were already out of
contention while Punjab needed a victory in their last match to keep their hopes alive.
Teja, dropped thrice during his 41-ball knock, hit two sixes and five fours in his team's final match, watched by spiritual leader the Dalai Lama who also met players before the start of the game.
He reached his half-century in style, hitting a six off leg-spinner Piyush Chawla who conceded 48 in his four overs. Deccan plundered 113 runs in the last 10 overs to set a stiff target.