Crusaders are in a strong position in the Setanta Cup semi-final thanks to a David Rainey double in the first leg.
Lee Lynch netted for Rovers but it was ruled offside while Crues striker Timmy Adamson wasted a close-range chance.
Rainey diverted Chris Morrow's fierce free-kick into the net to give the Irish League side a 41st minute lead.
Sligo had a penalty appeal turned down before the forward sealed the win with a powerful header from David McMaster's cross nine minutes from time.
Adamson scuffed his six-yard shot but it still required a good save from Gary Rogers to deny the attacker.
Rogers kept out an Adamson header before Rainey deflected Morrow's free-kick into the bottom corner for a deserved opener.
Sligo may top the Aitricity League standings but they failed to build any momentum at Seaview, although they were unlucky when a Colin Coates tackle on Raffaele Cretero did not result in a penalty.
Crusaders remained the more threatening and they scored a second goal through Rainey's header from six yards.
Cretaro saw a late shot saved by Sean O'Neil and Sligo now face an uphill task in next Monday's second leg at the Showgrounds.