Pacers Trent Boult (2/20) and Harshal Patel (1/23) - who contributed with the bat as well - helped Delhi seal the victory. Chennai started the chase well with in-form Ambati Rayudu scoring yet another quickfire half-century off just 29 balls but his dismissal by Patel completely changed the game.
The pitch slowed down as well which made the batsmen's job even more difficult. Watson struggled, scoring 14 off 23 balls. Lamichhane got the wicket of dangerous Raina, whose form will be a worry for Chennai. Dhoni was still at the crease and it seemed he would guide the team home but Delhi bowlers bowled well.
Boult then removed Dhoni for a sluggish 17 off 23 balls. Mishra and Lamichhane tossed the ball and got it to spin. Mishra accounted for Billings and Watson.
In the end, it was a comfortable 34-run for the home side.
Earlier, put into bat, Delhi were helped by late blitzkriegs from Vijay Shankar and Patel to help reach 162/5.
Shankar (36 not out from 28 balls) and Patel (36 not out from 16) milked 26 runs off the final over from Dwayne Bravo to forge a 65-run sixth wicket stand -- the highest of Delhi's innings -- and rescue the hosts from a troubled start.
Delhi were off to a sluggish start before losing in-form opener Prithvi Shaw off a run-a-ball 17 in the fifth over with the scoreboard showing 24 runs.
Shaw, who received a reprieve a couple of balls earlier when Shardul Thakur dropped a simple catch off Ravindra Jadeja, failed to cash on it and fell to Deepak Chahar with Thakur making no mistake this time around.
Shaw's dismissal brought together the in-form duo of skipper Shreyas Iyer (19 from 22; 4x3) and Rishabh Pant (38 from 26; 4x3, 6x2) and the right-left combo forged a 54-run second wicket stand to stabilise Delhi's innings.
While Iyer played the more sedate innings, Pant looked at his aggressive best punishing veteran off-spinner Harbhajan Singh for two sixes and a four.
But as things started going smoothly Delhi's way, South African Lungi Ngidi jolted the hosts by packing back both Iyer and Pant in a span of four deliveries.
Back into the attack for his second over, Ngidi cleaned up Iyer with a skiddy short of length delivery before enticing Pant with a short ball, which resulted in a top edge into the safe hands of Bravo at third man.
Struggling at 81/3, Glenn Maxwell and Shankar were assigned to resurrect the innings but form continued to elude the Australian who found his leg stick walking with a straight delivery from left-arm spinner Jadeja.
Delhi immediately lost another wicket in rookie Abhishek Sharma (2), whose top edge found the safe hands of Harbhajan at mid-on.
With half the side back in the hut at 97, Patel joined Shankar to strike a few lusty blows to take the side past the 150-run mark.
Shankar started slowly before picking Bravo for some special treatment over the fence before Patel joined the party in the final over by clobbering the West Indian for three maximums.
First Published: May 18, 2018, 11:55 PM IST