Dundalk won the battle of the First Division promotion chasers with a clinical performance at Tolka Park on Friday night.
Veteran Trevor Vaughan opened the scoring on 17 minutes from the penalty spot. Alan Keely, son of manager Dermot, was then sent off for Shelbourne.
Substiute Paul Crowley sealed Dundalk's place in the fourth round with two goals in the final 20 minutes.
