Alan Knill's side claimed a second successive win to move clear of the relegation zone and climb up the League Two table.
The Gulls were given a helping hand when they took the lead with a freak goal in the 28th minute. Rene Howe and Stewart Drummond challenged for the ball with the Morecambe defender passing back to his own goal only to see home keeper Barry Roche let the ball crawl under his feet and into the net.
The goal was an added blow for the Shrimps who found themselves a man down in the 23rd minute when teenage debutant Chris Doyle was shown a straight red card for hauling down Elliot Benyon.
To their credit Morecambe hit back with Ryan Williams testing Michael Poke with a dipping, swerving 40-yard free-kick.
The home side maintained the pressure at the start of the second half with defender Andy Wright hitting the post with a superb volley from the edge of the area.
Kevin Ellison then went close with a 30-yard volley that flew inches wide of the left-hand post before the Gulls doubled their advantage through Ashley Yeoman.
The substitute had only been on the field for a matter of seconds when he broke down the left and fired a low left footed shot past Roche.
Williams went close to adding a deserved consolation with an injury time free-kick which was excellently saved by Poke.