Bohemians 3 Drogheda United 0
Goals early and late from Robbie Doyle, Dave Morrison and Fergal Harkin booked Bohs' berth in their fifth FAI Cup semi-final in a row.
Bohs were quickest out of the blocks and took a 13th minute lead.
Skipper Kevin Hunt's cross in from the right took a deflection before Glen Crowe flicked it on to Robbie Doyle whose weak header still beat a disappointed Gary Rogers.
Man of the match Morrison finally sealed the win on 82 minutes when cutting in from the left to curl a shot to the top corner.
Drogheda's sad night continued five minutes later when defender Pat Scully was sent off for a lunging tackle on Paul Keegan.
Fergal Harkin then added Bohs' third goal in stoppage time as they go through to Thrusday's semi-final draw along with Galway United, St. Patrick's Athletic and Longford Town.