The Addicks made a dream start by taking the lead in the third minute. Paul Hayes' pass found Bradley Wright-Phillips 20 yards from goal and the prolific striker scored his fourth goal of the campaign by firing an unstoppable drive beyond the reach of visiting keeper Richard O'Donnell.
Dale Stephens blazed over from eight yards after Wright-Phillips' poor clearance was played into his path by a Wednesday defender.
Owls boss Gary Megson was clearly unimpressed by his side's poor start and replaced Chris Sedgwick with Ryan Lowe after just 22 minutes.
Lowe suffered an injury early in the second half and ironically found himself replaced by Morrison in the 53rd minute.
And it was Morrison who drew his side level three minutes later when the veteran striker headed home a Chris Lines corner before running the full length of the pitch to celebrate in front of the visiting fans.