The win takes David Jeffrey's side three points clear at the top of Group Two.
Young striker Peter Steele almost put Glentoran 2-0 ahead when he went clear after 23 minutes but his shot was blocked by a last-ditch challange from Stephen Douglas.
Linfield squandered a number of chances before the leveller - Oran Kearney's high cross was dropped by Dougherty and McAreavey capitalised.
The midfielder completed his double by drilling low into the bottom corner from 16 yards.
Dickson's strike for the third goal lacked power but Dougherty was slow to react as the ball sneaked in.
Blues keeper Alan Mannus produced an excellent save to keep out Dean Fitzgerald's shot on 71 minutes.
Linfield wasted late opportunities to extend their advantage but the points were safe.
The focus now turns to the Carnegie Premier League clash between the Big Two at Windsor Park.
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