The result brings an end to Deccan’s unbeaten run and sets Delhi on course for the semi-finals.
Delhi’s decision to field first paid off at the start of the innings as Deccan openers Adam Gilchrist and Herschelle Gibbs were prised out with just eight on the board.
Gilchrist miscued a pull and was caught by keeper Dinesh Karthik and Gibbs mishit a drive to AB De Villiers at mid off to hand Nannes the second wicket of a fiery spell of bowling.
Akash Bilakhia and Rohit Sharma rebuilt the innings with a partnership of 33, but both fell to Delhi’s spinners.
Daniel Vettori trapped Bilakhia (22) lbw and Sharma (17) fell to Asish Mishra when looking set to cut loose.
The much-maligned strategy break has been the scourge of the batsmen in The IPL, but for the first time it knocked a bowling side off their stride.
Dwayne Smith, a West Indian who thrills and frustrates in equal measure, launched a brutal assault on Vettori, Mishra and Dilshan.
Smith produced some clean hitting in his 48 from 28 balls and aided by Tirumalsetti Suman (23), he guided his side to 148 in their 20 overs.
Delhi’s bowlers more than justified Virender Sehwag’s decision to bowl first, with Nannes giving the Australian selectors a nudge with 2-16 from his 4 overs.
Sehwag and Gautham Gambhir have not clicked yet in The IPL and again they flattered to deceive against Deccan.
Sehwag played a couple of cracking cuts and flicks before picking out Gibbs at point off RP Singh and Gambhir was controversially dismissed lbw off Shoaib Ahmed.
De Villiers played a rash shot off Shoaib and was caught by Pragyan Ojha at mid-off, but Dilshan and Karthik regrouped with a superb partnership of 79.
Sandeep Lamichhane handed first Delhi Daredevils cap