Delhi scored 173-7 before restricting Deccan to 161 despite Gilchrist´s 33-ball 64 to boost their chances of qualifying for the semi-finals.
Delhi lead the eight-team competition with 16 points from 10 matches, followed by Chennai (13/10), Deccan (12/11), Mumbai (11/11), Rajasthan (11/11), Bangalore (10/11), Punjab (10/11) and Kolkata (3/11).
The top four sides will advance to the semi-finals.
Gilchrist went for his shots from the beginning, hitting seamer Ashish Nehra for four boundaries in the opening over. He cracked five sixes and as many fours before inside-edging seamer Pradeep Sangwan´s delivery on to his stumps.
Andrew Symonds kept the momentum with a 22-ball 41 before seamer Rajat Bhatia (4-15) triggered a dramatic collapse which saw Deccan lose their last seven wickets for just 12 runs.
Dinesh Karthik earlier helped Delhi set a stiff target with a 23-ball 44 not out, including 18 runs off the last five deliveries from Sri Lankan paceman Chaminda Vaas.
Sri Lankan Tillakaratne Dilshan set the pace, plundering 24 runs in an over from paceman Shoaib Ahmed. He cracked one six and seven fours in his 18-ball 37 before being caught by Ravi Teja in the deep off Symonds.
South African AB de Villiers kept the scoreboard moving after Dilshan´s dismissal, scoring a 36-ball 44.
Smith's batting may force rewriting of manuals - Gilchrist
