CSK skipper Mahendra Singh Dhoni's (30) and his Indian teammate Ravichandran Ashwin (12*) guided his team to a modest total of 150 ruins for the loss of seven wickets.
CSK bowlers restricted Delhi for 149 runs for the loss of nine wickets as they gifted a thrilling encounter to the spectators.
MS Dhoni hit two sixes during his knock of 30 runs.
A lacklustre batting performance by Delhi Daredevils' top order batsmen meant that the onus was on Albie Morkel to see them through as Yuvraj Singh (9) and JP Duminy (5) also failed to shine with the bat.
Albie Morkel's 73 off 55 almost won them the match but his team fell a run too short of the required target at the end of twenty overs.
CSK's pacer Ashish Nehra put up a strong performance as he took up three wickets by giving away 25 runs.
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