Chennai won the toss in Raipur and opted to bat, but it was a decision that didn't pay off as their innings never really got going.
Openers Dwayne Smith (18) and Brendon McCullum (11) both scored at less than a run a ball before Faf du Plessis and MS Dhoni put on a 37-run fourth-wicket partnership to push the visitors towards 100.
In the end, they posted just 119-6 from their 20 overs. Zaheer Khan was the pick of the Delhi bowlers as he took two wickets for just nine runs from his four overs, including 19 dot balls.
Delhi's response didn't start well as Ishwar Pandey took the early wickets of South Africans Quinton de Kock (3) and JP Duminy (6), but Shreyas Iyer and Yuvraj Singh's third-wicket stand of 69 put the hosts in full control.
Iyer hit the winning run to finish on 70 not out as Delhi, who have no chance of reaching the playoffs, achieved the victory target with 20 balls to spare.
Chennai could have secured their place in the playoffs with a win, but they are still well on course to finish in the top four.