Delhi never found momentum once it lost captain David Warner without scoring before it got restricted at 140-8.
Chennai, which won the toss and elected to bat, struggled in the first half but Ravindra Jadeja (21) and captain Mahendra Singh Dhoni (20) lifted the total to 167-8.
Chennai moved to No. 2 with 15 points behind table-topper Gujarat Titans (16 points). The defeat pushed Delhi to the brink of elimination from the playoff race with eight points from 11 games.
Warner was outdone by the slowness of the pitch as he gave a straightforward catch to Ajinkya Rahane in the covers off fast bowler Deepak Chahar’s second ball.
Chahar struck again in the powerplay when Phil Salt (17) top-edged at mid-on and Mitchell Marsh (5) got run-out in a mixup with impact player Manish Pandey as Delhi slipped to 25-3 in the fourth over.
Pandey and Rilee Rossouw (35) combined in a half-century stand but both batters got tied down by spinner Jadeja (1-19) and Moeen Ali (0-16) before Sri Lanka fast bowler Matheesha Pathirana (3-37) choked Delhi further with his brilliant yorkers in the latter half.
Pathirana had Pandey leg before wicket with a superb yorker in his first over and also claimed the wickets of Axar Patel and Lalit Yadav with change of pace to cap a brilliant all-round show by the home team.
Earlier, Devon Conway couldn’t capitalize on some early close calls before he was trapped lbw by left-arm spinner Patel (2-27) off his first ball.
Delhi didn’t go for a television referral when Khaleel Ahmed found a thin outside of Conway’s bat before the left-handed opener survived lbw referral against off-spinner Lalit Yadav.
Patel also accounted for the wicket of Ruturaj Gaikwad (24) in his second over and then Yadav took a splendid low one-handed return catch of Rahane off his own bowling as Delhi continued to strike with regular intervals.
Delhi looked to have contained Chennai when Ambati Rayudu (23) fell in the 17th over but Jadeja and Dhoni smashed two boundaries and three sixes between them to propel the team’s total in the last three overs.
Meanwhile, Dhoni was unhappy with the performance of his batters. He took a dig at them for playing reckless shots.
“Some of the batters played reckless shots which resulted in fall of wickets. They should understand the value of staying at the crease. You can only score runs on a slow track when you stay there,” he said.