Hussey (65 not out) and Mahendra Singh Dhoni (44) pushed Chennai to 169 for four and pacer Sharma led the bowlers' charge to dismiss the hosts for 83, the lowest total so far in IPL 6.
Delhi remain winless in the competition with six losses in as many games. Chennai would welcome the result after their shock loss against the Pune Warriors Monday. They now have three wins from five matches.
Openers David Warner and Virender Sehwag (17) had to fire to give Delhi a chance of surpassing the steep target. But that did not happen as Sharma sent the dangerous duo back in the hut by the sixth over.
Sehwag getting caught at mid wicket made it 30 for four, meaning Delhi had lost all their key batsmen. Manpreet Juneja also fell to Sharma while skipper Mahela Jayawardene was adjudged leg before off Chris Morris.
Kedhar Jadhav (31) and Jeevan Mendis (12) provided brief resistance before succumbing to the pressure of mounting run rate. The Sri Lanka's run out left Delhi needing 108 from the last nine overs. Chennai knew they had sealed it by then.
Earlier, the visitors made a subdued start with Hussey and Suresh Raina (30) taking the team to 60 for one in 10 overs.
Realising the need for acceleration, the two southpaws changed gears. Raina freed his arms to hit two successive fours off Umesh Yadav and Hussey followed suit in the next over, punishing Ajit Agarkar for a six and four.
Raina was soon caught behind off Irfan Pathan, leading to Dhoni's arrival in the middle.
Much to the delight of fans, Dhoni promoted himself to number four in the batting order. He opened his account by spanking Pathan for a boundary over mid-wicket. It was a run feast from there on.
Big shots from Dhoni and Hussey's bats became a routine. The crowd turned wild when Dhoni smashed Morne Morkel for a six and four in the 17th over which eventually went for 19 runs. He also had luck on his side as he was dropped by Ajit Agarkar on 19.
Dhoni was dismissed in the 20th over but not before he dished out his trademark helicopter shot.
Hussey, who missed the last game, crafted his innings beautifully. His 50-ball effort comprised six fours and a couple of sixes.
Chennai ended amassing 109 runs in the second half of their innings.