The home side led two-nil with 20 minutes remaining and looked set for their first home win of the season, but a Ross Jenkins wonder goal and two penalties from Warren Feeney gave Argyle a memorable victory - their first on their travels.
Morecambe had the best possible start when they went a goal up after just four minutes. Jack Redshaw robbed Darren Purse of possession as the experienced defender lingered and the young striker took full advantage to run into the box and slot past Jake Cole from the tightest of angles.
The Shrimps survived an early second-half onslaught before duly going two-nil ahead when substitute Richard Brodie was felled in the box by Durrell Berry, leaving the striker to convert past Cole.
That inspired Argyle who upped a gear and Jenkins' superb' 72nd-minute strike from distance halved the deficit, before the visitors won a penalty when Izak Reid was unfortunate to handle Alex MacDonald's right-wing cross.
Referee Tony Harrington was then forced to point to the spot for a third time late on when Andy Parrish brought down Paris Cowan-Hall with a rash challenge, Feeney keeping his cool to again score from 12 yards.