The leg spinner's two for 16 helped Kings XI Punjab restrict Delhi Daredevils to a paltry 111 at a sluggish track of Ferozeshah Kotla after home team captain Gautam Gambhir won the toss and elected to bat.
Irfan Pathan - who had figures of three for 24 - removed Virender Sehwag for a golden duck in the second over.
Captain Gautam Gambhir (26) and David Warner (6) tried to repair the damage to an extent.
But some superlative effort by the Punjab fielders helped their side affect two run-outs at a crucial juncture reduced Delhi to 41 for three in 4.1 overs.
Paul Collingwood (4) and Dinesh Karthik (17) then added 14 runs but Chawla struck twice, trapping the former leg before and rattling Daniel Vettori's stumps (2) - both with googlies - as Delhi lost half of their side for 63 in 10 overs.
They never recovered from that slump.
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Images: Kings XI Punjab vs Mumbai Indians
Images: Delhi Daredevils vs Rajasthan Royals