Kennedy struck with 18 minutes to go after George Donnelly's left foot effort was superbly saved by Morecambe keeper Barry Roche and rebounded into his path at the far post.
Andy Fleming gave Morecambe the lead on 12 minutes with an excellent strike from 20 yards out. The midfielder took the ball in space and took full advantage with a low drive that beat Josh Lillis low to his right hand side.
The first half was full of talking points with Morecambe on top for the start of the game before Rochdale took control and forced home keeper
Roche into a string of top quality saves.
Roche was beaten by an excellent Bobby Grant free kick on 32 minutes but the ball crashed against the Morecambe crossbar.
Grant was Dale's biggest threat with three efforts well saved by the Morecambe keeper whose best save came from a looping Ryan Edwards header that was heading for the top left hand corner until Roche twisted his body and saved at full stretch.