The strike bowler, one of four South Africans in action in the match, took 3-18 as Kolkata, who were sent in to bat, were restricted to 97 for nine in their 12 overs in a rain-reduced match.
Morkel’s batsmen then made slightly heavy weather of the chase and it needed new-ball bowler Irfan Pathan’s 42 not out off just 20 balls to see Delhi home with five balls remaining.
After captain Virender Sehwag was well-caught by Iqbal Abdulla, running around the long-on boundary, off Rajat Bhatia for 20 off 13 balls, the Daredevils were 57 for two in the eighth over, needing 41 off 28 balls.
Medium-pacer Bhatia finished the over well and Delhi needed 39 off the last four overs, with Irfan having faced just four balls.
But he hit Jacques Kallis for six in the next over and then he hammered Marchant de Lange for two more sixes in the 10th over to get the required run-rate down to less than a run-a-ball.
It was surprising that Kolkata captain Gautam Gambhir decided to bowl the inexperienced De Lange in the 11th over, the rookie South African conceding 17 runs as he bowled too short to Irfan, with the vastly-experienced Brett Lee still having an over left.
Aaron Finch scored 30 to ensure the Daredevils were off to a solid start, before Kallis (3-0-23-1) bowled a precise cutter to bowl the Australian.
De Lange had done much to ruffle the batsmen with some fiery bowling but Irfan was able to take his team home.
Delhi Daredevils fast bowlers Morkel and Umesh Yadav had earlier crippled the Kolkata Knight Riders innings as they restricted them to 97 for nine in their 12 overs.
Morkel set the tone for the Daredevils’ dominance as he bowled Kallis (4) and Manoj Tiwary (0) with brilliant yorkers off successive deliveries on his way to superb figures of three for 18 in his three overs.
The South African giant had an impressive supporter in Indian star Yadav, who took two for nine in two overs, conceding just three runs in the penultimate over and claiming the wicket of top-scorer Laxmi Shukla for 26.
The match was played over 12-overs-a-side after a rain delay of two-and-a-half hours in Kolkata and, after being sent in to bat, the Knight Riders were quickly in trouble as Morkel and Roelof van der Merwe, his teammate at the Titans, reduced them to 20 for three after three overs.
Left-arm spinner Van der Merwe trapped Brendon McCullum lbw for nine before Morkel’s double-strike. Things only got worse for the Knight Riders as Yadav, who is not short of pace, had Yusuf Pathan caught behind for a duck as he got himself into a tangle against a short-pitched delivery.
Morkel, who took 6-23 in national colours in his last outing, then returned to bowl Indian star Gambhir, who failed to handle the extra bounce and chopped on, for 16.
Kolkata were 54 for five, but the Daredevils were guilty of taking their foot off the throat a bit as Debabrata Das was dropped on two and Shukla was able to hammer a four and two sixes.
Das scored 18 off nine balls and Shukla 26 off 17 but not even their efforts could save Kolkata from a half-baked innings.
Excellent bowling at the death by Yadav and Van der Merwe ensured that the Knight Riders’ run-rate never rose to any great extent, despite some lusty blows by Das and Shukla.
Morkel was obviously the best of the Delhi bowlers, but the efforts of Yadav and Van der Merwe (two for 28) were also of great value.