Anthony O’Connor opened the scoring in the second minute and fellow defender Carl McHugh made it two just after the hour mark.
Vadaine Oliver’s acrobatic goal set up a tense finish, but Argyle held on to move up to seventh.
The recalled O’Connor opened the scoring with his first touch of the ball, meeting Bobby Reid’s floated free-kick from the left with a superb looping header that beat Stags goalkeeper Sascha Studer.
Argyle failed to build on their early advantage and in the 22nd minute home keeper Luke McCormick made a fine diving save to keep out Reggie Lambe’s volley from Chris Clements’ corner.
Mansfield had the better of the first-half chances with Lambe firing just over as the interval approached and Oliver smashing a shot inches wide in stoppage time.
But the hosts doubled their lead when McHugh glanced in a near post header from Reid’s corner in the 63rd minute.
A minute later Mansfield striker Oliver scored with a superb volleyed bicycle kick after his initial headed effort came back off the post.
But the Stags could not find a late equaliser and remain six points above the relegation zone.