The former Blackpool and Coventry hitman's ninth goal of the season did the damage as the hosts maintained their League Two promotion push.
A lung-bursting run from skipper Stephen Dawson led to the goal. The midfielder found Elliott Bennett on the right and the winger chipped the ball over Shwan Jalal's head leaving Morrell the simple task of firing into the empty net.
Knill's men could have won by more after piling on the pressure in the second half following Morrell's opener.
Centre-back Ben Futcher headed against the crossbar and Bournemouth keeper Jalal was forced to make a string of fine saves to keep his team in the contest.
The first-half had produced few clear-cut chances although Bennett came close for the Shakers when he fired over the bar from the edge of the box.