IT took Nasser Hussain's side 169 overs to eventually bowled India out for 469.
Yorkshire spinner Dawson claimed four wickets, with three in the final six of his 43 overs.
County colleague Matthew Hoggard finished the innings less than an hour after tea to finish with three for 98.
But 21-year-old Dawson, on his Test debut, belied the fact he had played only nine first-class games for Yorkshire.
"I thought the biggest plus was his temperament, bowling at world-class players on a pitch that didn't help him particularly," said Dilley.
"He bowled with control. That suggests there is a big future for him in the game. Someone with that sort of temperament can go on."
Dawson, in fact, could have repeated the performance of Indian spinner Harbhajan Singh with a five-wicket haul but for some slacking in the field.
James Foster missed a straightforward stumping chance when Saurav Ganguly advanced down the wicket and Graham Thorpe dropped a regulation catch at cover from Sanjay Bangar.
"We bowled with discipline and control, aggression when needed, but overall patience," added Dilley.
"We created some chances that weren't taken and if you do that here you are going to be in the field an awfully long time."
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