The former Dewsbury Rangers player netted twice inside the first ten minutes at Elland Road to put his side on the way to victory in the fourth round tie.
He completed his treble in the second half from the penalty spot as Richard Naylor’s men ran riot in front of goal.
Whites captain Alex Mowatt, Afolabi Coker and Eoghan Stokes completed the scoring for the hosts, who will face either Liverpool or Histon in the fifth round.
Dawson signed his first professional contract with Leeds earlier this season and was included in Neil Warnock’s first-team squad for the Whites’ Championship clash against Watford in November.