Sligo eased into the quarter-finals with a defeat of 10-man Mervue United in front of 1,205 at the Showgrounds.
Barry O'Mahony was shown a straight red card by referee Tomas Connolly after just 18 minutes, when he handled on the line to prevent Anthony Elding's header going in.
The striker dispatched the spot-kick and Rovers were never in any real danger after that.
The visitors only threatened through a Brendan Lavelle snapshot in the opening half, but Rovers had few chances themselves, though Lee Lynch forced a fine save from Conor Gleeson just before the break.
The second goal eventually came on the hour-mark, as Evan McMillan headed home his second of the season from a Joseph Ndo corner.
The third followed 10 minutes later as Danny Ventre finished after great play by Alan Keane and Raffaele Cretaro.
Rovers' fourth was the best of the lot as Elding fired home a thunderbolt from outside the area in injury-time.
Sligo – Rogers, Keane (Owens 80), Henderson, McMillan, Gaynor, Ndo (Martin 71), Lynch, Ventre, Cretaro (Djilali 71), Greene, Elding.
Mervue – Gleeson, McSweeney, Woods, Walshe, Kenny (Siambanda 68), Kelly, O'Mahony, Curran (Varley 38), Sinnott, Lee (Manning h-t), Lavelle.
Ref – T Connolly.