The Shrimps had a dream start with two goals in the first 10 minutes and never looked in danger from there.
Kevin Ellison gave them the lead after six minutes as Barnet conceded for the first time in five games. Ellison was given space on the right hand side of the box and cut inside on to his left foot to fire an effort in on goal that took a wicked deflection to wrong foot Barnet goalkeeper Graham Stack.
Four minutes later it was 2-0 with a well worked goal.
Gary McDonald threaded in the perfect through ball for Andy Fleming, who ran into the box and produced a right foot shot from the angle that gave Stack no chance.
The Shrimps sealed the win with two late penalties from Richard Brodie after fouls by Barry Fuller and Krystian Pearce before Jon Nurse claimed an injury time consolation when he stabbed the ball home from close range after the home defence failed to clear a Mark Byrne corner.