Cherries captain Pearce headed home Brett Pitman's free-kick from 10 yards in the 48th minute and it proved to be enough to secure all three points and consign Aldershot to their third consecutive defeat.
Aldershot were dangerous on the break and Marvin Morgan had a goal ruled out for offside in the 34th minute and then had a low right-foot shot saved by Bournemouth goalkeeper Shwan Jalal.
After Pearce's goal, Steve Fletcher had a header saved and Liam Feeney was denied by a good save from Mikhael Jaimez-Ruiz.
Aldershot came back into the match and substitute Danny Hylton should have scored in the 65th minute after being set up by Kirk Hudson but his shot from 12 yards was comfortably saved by Jalal.
Shots midfielder John Halls went close with six minutes remaining with a fierce right-foot shot that flashed just over the bar and at the other end Mark Molesley was denied a goal against his former club by another good stop from Jaimez-Ruiz.