Anthony O’Connor scored a 54th-minute opener from Bobby Reid’s corner seconds after James Shea had made a brilliant fingertip stop to deny Lewis Alessandra.
O’Connor tapped in at the far post as Reid’s corner landed at the Irishman’s feet.
Ade Azeez replied from close range in the 63rd minute after keeper Luke McCormick saved substitute Craig Tanner’s initial shot.
Wimbledon started brighter than their hosts with George Francomb curling a a shot from the left just past the post.
Argyle responded with Gethin Jones bouncing a cross-shot off the bar and playmaker Bobby Reid forcing a full length save from Shea.
Plymouth continued to press in the second half with Shea making a brilliant diving save to turn an on-target Alessandra shot around the post.
From the corner Carl McHugh’s near post goal bound header was flapped over by in-form Shea.
Alessandra hammered a 15-yard shot just wide in the 85th minute while Sean Rigg forced a superb diving save from McCormick in stoppage time.