Glentoran were reduced to ten men in the 40th minute after Mark Glendinning was given his marching orders and a minute later they were further behind as Peter Thompson struck for Linfield.
The second half was all Linfield and two goals from Paul McAreavey, a second for Thompson and another for William Murphy made it 6-0.
The victory sees Linfield finish top of Group 2 to guarantee a home tie in the semi-finals.