South African allrounder Morris took 2-35 from his four overs as the Lions racked up a commanding 6-172 thanks to brilliant 60 from 36 balls by former New Zealand skipper Brendon McCullum that included three sixes and six fours.
Dwayne Smith was equally brutal with 53 off 30 deliveries as the pair put on 112 for the opening wicket before the Daredevils put the brakes on the assault with three wickets for five runs before Australia's James Faulkner added 22 valuable runs with some lower order hitting.
Delhi got their response off to a disastrous start as Dhawal Kulkami ripped through the top order to reduce the hosts to 3-16.
Rishabh Pant's departure for 20 left the Daredevils foundering at 4-57 but the arrival of Morris at the crease along with his Proteas teammate JP Duminy changed the complexion of the match.
Morris' half-century came from just 17 balls on his way to an unbeaten 82 that included eight sixes and four boundaries.
Duminy was then dismissed for 48 after being caught and bowled by Dwayne Bravo and a superb penultimate over from Praveen Kumar that yielded just five runs followed to leave the home side needing 14 from the last over.
Morris sent the first ball of the final over bowled by Bravo to the fence following a dropped catch by Faulkner, but the West Indies star managed to hold his nerve as the Daredevils slipped to only their second loss of the season.
