Ghana triumphant on Essien return
The Chelsea midfielder, back for the first time since the 2010 finals after ending a self-imposed exile, set up an early chance with a rasping shot that the visiting goalkeeper spilled.
Ghana struck two quickfire goals midway through the second half thanks to Isaac Vorsah and Prince Tagoe.
Matt Moussilou took advantage of a mistake by goalkeeper Richard Kingson to pull a goal back for Congo with 15 minutes left but Emmanuel Agyemang-Badu made it 3-1 to Ghana with a long-range shot.
Leaders Ghana have 10 points from four games in Group I followed by Sudan on seven. Second from bottom Congo, who have three points, can no longer qualify.
Sudan visit Swaziland on Sunday.