Argyle captain Conor Hourihane cracked a 20-yard rising drive past diving 'keeper Barry Roche to make it 1-0 after 10 minutes.
It was a huge fillip for the home side and within six minutes Argyle were 2-0 up following a sweeping move down the left.
On-loan Ipswich striker Ronan Murray raced on to a throughball before firing over a superb, pacy cross which was turned in off the far post by Paris Cowan-Hall by way of a deft flick.
Morecambe threatened and experienced midfielder Kevin Ellison had a 29th-minute shot cleared off the line by man of the match Hourihane.
Plymouth 'keeper Rene Gilmartin punched away Ryan Williams' goalbound free-kick after 70 minutes but could do nothing to keep out the Shrimps substitute's 80th-minute long-range strike, which made it 2-1.
Morecambe were reduced to 10 men in the 85th minute when midfielder Andrew Parrish was sent off for a foul on Onismor Bhasera.
But they found experienced central defender Guy Branston, 34 in midweek, in top form and failed to force an equaliser.