Coke struck from the edge of the area after receiving Morrison's lay-off in the 62nd minute, and Morrison made it 2-0 seven minutes from time with a glancing header following Tommy Miller's chip into the area for the Owls' third straight victory.
Rochdale made a bright start to the match with Nicky Weaver forced to save from Joe Thompson and Gary Jones.
Wednesday improved towards the end of the first half with Neil Mellor heading against the crossbar from Morrison's cross.
But Coke fired the Owls ahead before Thompson spurned a great chance to equalise, clipping the ball wide after side-stepping Weaver.
Morrison's goal then sealed the victory for Wednesday and left Rochdale with just one win from their last seven games.