Kings XI first rode on David Miller and captain Adam Gilchrist's whirlwind knocks to post a challenging 171 for four.
Miller scored an unbeaten 44 off just 24 balls towards the end, while Gilchrist made 42 off 26 balls upfront. Shaun Marsh also played a sedate 44-ball 45-run knock to help Kings XI's cause.
Defending the total, Sandeep Sharma returned with figures of three for 23 to help Kings XI restrict Daredevils to 164 for seven.
While Chand was bowled by Praveen Kumar, Pathan and Warner were picked up by Sandeep in successive balls in the last two deliveries of the fourth over.
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Pathan edged a swinging delivery to Gilchrist behind the stumps and then a ball later Warner departed without opening his account, caught by Marsh in the slips.
Skipper Mahela Jayawardene (39) and Virender Sehwag (30) shared 49 runs off 40 balls for the fourth wicket before the latter edged one to Gilchrist off Parvinder Awana's bowling.
Jayawardene and Ben Rohrer (49) then added quick 50 runs off 5.3 overs to keep Delhi's hopes alive.
The ever-climbing asking rate finally took a toll on Jayawardene, who was caught by Manan Vohra to give Sandeep his third wicket of the day. He hit three fours and a six during his 42-ball knock.
But Rohrer kept Delhi in the hunt as, needing 41 off 12 balls, the left-hander picked up 19 runs of the penultimate over off Azhar Mahmood to bring dowm the equation to 22 off the final six deliveries.