Glentoran moved up to fifth in the Premiership table thanks to a comfortable success at New Grosvenor.
Sean Ward gave Eddie Patterson's men a 25th-minute lead with a shot that was deflected past keeper Lee Windrum.
Jimmy Callacher had a header cleared off the line while Jordan Hughes was wide with a good chance for Distillery.
Richard Clarke shot in Glentoran's second on the hour and then former Whites striker Andrew Waterworth headed in from Stephen Carson's cross for 3-0.
Lisburn Distillery are now five points adrift at the foot of the Premiership table as one-from-bottom Donegal Celtic picked up a good point away to fourth-placed Coleraine.
Tim McCann's men are in Irish Cup action on Tuesday night when they entertain Dundela in a rearranged last 16 clash.
Distillery led 3-0 in the first meeting last week but the match as abandoned because of thick fog.