Stephen Kenny’s side were always on top against their First Division opponents with an own goal and strikes from Jake Kelly, Kurtis Byrne, Richie Towell and Ronan Finn seeing them win comfortably.
Shelbourne’s best hope of causing an upset came in the 11th minute when Alan O’Sullivan seized on a Paddy Barrett mistake to burst through only to see his shot clip the post.
That miss was to prove costly as Ryan Robinson headed a cross from Finn into his own net three minutes later.
Dundalk then doubled their advantage in the 22nd minute when Towell’s cross from the right was headed to the bottom right hand corner of the net by Kelly.
It took the Louth men until four minutes after the restart to add to their lead when Byrne prodded home from close range after the ball was flicked on by Shane Grimes.
Barrett then had a header cleared off the line by Dylan McGlade before Shelbourne substitute Jake Donnelly brought the only save of the match from Gabriel Sava in the 68th minute.
Towell made it four from the penalty spot in the 71st minute after substitute Ciaran O’Connor was felled by Colm Crowe and the teenager would also have a hand in the fifth eight minutes later when he kept a Sean Gannon cross alive for Finn to head home.
Sava; Gannon (McMillan 81), Barrett, Boyle, Grimes; Kelly, Mountney, Towell (Shields 75), Horgan (O’Connor 64); Finn, Byrne.
Murray; O’Connor, (Gannon 79), Robinson, Heaney, Osam; O’Sullivan, Crowe, Doyle, Walsh (J Donnelly 63), McGlade; Sandford (Hughes 71).
D McKeon (Dublin).