Goals from Gary McCabe, Ciaran Kilduff, Kieran Marty Waters, and Eamon Zayed helped Trevor Croly's side reach the FAI Ford Cup third round
The SSE Airtricity Premier Division outfit controlled the match from the outset, opening the scoring after just two minutes when Gary McCabe finished from Ronan Finn's cross. Four minutes later, they doubled their lead through Ciaran Kilduff, who headed home from close range.
After the slow start, Sheriff YC battled their way back into the game, but the Hoops' greater calibre shone through after the interval when Kieran Marty Waters slotted the ball home to extend the visitors' lead.
Substitute Eamon Zayed completed the rout on 64 minutes, after Finn played him in with an excellent ball. After sealing their progress in the next round of the cup, Shamrock Rovers now turn their attentions to Friday's league game with Cork City.