The result looked unlikely as Cameron White threatened to bludgeon Deccan's home with a knock of 77, that included nine boundaries and two sixes, on a slow pitch.
White and Shikhar Dhawan were on course to overhaul the target of 161 but tight bowling and good fielding by MS Dhoni's men ensured victory and prevented a third straight loss for the home side.
Dhoni himself ran out key man White while the Australian was trying to steal a second run in the penultimate over after man of the match Suresh Raina took a brilliant return catch to dismiss Kumar Sangakkara.
The Deccan captain Sangakkara said that fielding made the difference.
"We got a good start today, but [Chennai] came back well with some good fielding," said the Sri Lankan batsman. "White batted well, but we dropped far too many to win a close game.
"We batted and bowled well but our fielding has cost us many games this season."
White's innings continued his recent renaissance, after his 78 against the Pune Warriors last week, to help end a horror form slump that has seen him dumped as Australia Twenty20 captain and exiled from their limited overs teams in the past six months.
Earlier, Dhoni won the toss and elected to bat in extreme humid conditions.
"The wicket has become slower," he said. "It was difficult for us to capitalise in the latter overs, because of the pitch. It is happening now; it happened last Champions League as well."
Super Kings top-scorer Faf du Faf du Plessis again led the way as his 45 at the top of the order, plus solid contributions from India duo Dhoni (34) and Raina (32), ensured a solid 160 for six, meaning Deccan were chasing eight runs an over.
An example of Deccan's poor fielding came when Dwayne Bravo was dropped by Sangakkara when he was run into by wicketkeeper Parthiv Patel just as he was about to take the catch. Bravo hit a six off the next ball.
Though Chennai were able to move into the IPL play-off places, Raina feels the team has more work to do.
"I think I need to spend more time at the crease. I am hitting well but need to bat till the 15th over," he said.
"We need to bat well, put some good scores on the board and defend well."
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