Electing to bat first, Kolkata were hoping for a good start, but the 23-year-old Tamil Nadu spinner ruined all their plans by claiming two wickets in his second over.
Chris Gayle [ Images ] slammed Ashwin for a huge six over long-on, but the bowler had his revenge off the very next delivery. The West Indies [ Images ] ace went for another big shot but was beaten in flight and stumped by wicketkeeper Mahendra Singh Dhoni [ Images ] after scoring seven.
In the same over, Ashwin dealt the visitors another big blow, claiming the wicket of Brendon McCullum [ Images ]. The New Zealander had no clue about the first four deliveries he received from Ashwin before top-edging a sweep to Muttiah Muralitharan [ Images ] at short fine leg. He was out for a duck.
Doug Bollinger complimented him well from the other end as he not only blocked one end up but also claimed the big wicket of Sourav Ganguly [ Images ], who was trapped leg before wicket for 10.
Wicketkeeper Dhoni's sharp glove work gave Ashwin his third wicket as David Hussey [ Images ] was stumped down the leg side for a duck. The youngster was unlucky not to bag a hat-trick as Angelo Mathews [ Images ] gloved one to the fielder at leg slip, but umpire Simon Taufel turned down the appeal.
He bowled four overs on the trot to register wonderful figures of three for 16 in fours as Kolkata were reduced to 30 for four after seven overs and never really recovered from that horrible start.
Having post a modest 139 for eight in their 20 overs, Kolkata never really threatened with the ball.
Suresh Raina [ Images ] led the way with the bat with a smashing innings of 78 from 39 balls, laced with 11 boundaries and three sixes. After Matthew Hayden's [ Images ] wicket for a duck in the first over, there was no further joy for the Kolkata bowlers.
Raina dominated with the bat, hitting boundaries at will, during his blazing partnership of 137 runs in 78 deliveries for the second wicket with Murali Vijay [ Images ], who proved the perfect foil with a brisk 50 from 40 balls.
On a day when Muttiah Muralitharan failed to sparkle, being hit for 47 in his four overs, Ashwin came up with a dream spell to keep his team's hopes alive of making it to the semi-finals.
Chennai crushed Kolkata by a whopping nine-wicket margin to jump to second in the standings.