The Glovers got off to a flyer, with Jake Gray netting the opener after just 22 seconds before Otis Khan doubled the lead on 17 minutes with a well-measured strike.
In the driving seat at the break, Town came out of a five-goal second half on the side of defeat after a frantic final 20 minutes.
Vadaine Oliver and Callum Lang made it 2-2, before Omar Sowunmi restored the visitors lead with six minutes left.
However, virtually from the restart Lang notched his second to tee up a grandstand finish as Kevin Ellison headed home a 93rd-minute winner for the Shrimps.
Darren Way was forced to make changes to his starting eleven for the first time in four matches with both James Bailey (knee) and Ryan Dickson (ill) unavailable.
Bailey picked up a medial knee ligament injury at Cheltenham on Boxing Day forcing him to miss his first league match of the season.
Connor Smith took the captain’s place in midfield, whilst Bevis Mugabi came into the back four.
In Bailey’s absence, Francois Zoko lead the Green and Whites out on his 97th Yeovil appearance.
Having made the 230-mile trip to Lancashire the visitors showed no signs of lethargy, rippling the net within the first 30 seconds.
Winning the ball from kick-off, Gray showed early quality to drive into the box and blast a rasping effort past Roche before many had even taken to their seats.
Stunned by conceding in the opening exchanges, the hosts took 10 minutes to regain their composure.
Slow to get going Jim Bentley’s side almost found an equaliser following a brief spell of pressure.
The veteran Ellison blasted over the bar from inside the box, before strike partner Oliver crashed an audacious shot on the turn from 35 yards onto the post.
Almost netting an equaliser from nowhere, any momentum the Shrimps were gathering was shattered before the 20-minute mark.
Always a bright spark in midfield, Khan burst into the box following a positive run, completed a quick one-two with Gray – who turned provider – before curling a pinpoint effort into the top corner to extend a glorious start to proceedings in Lancashire.
Oozing with confidence, the Glovers displayed some intricate passing on a soggy Globe Arena pitch, all the while ensuring Artur Krysiak remained untested between the sticks.
Already on a yellow for persistently fouling the lively Sam Surridge, Morecambe’s Max Muller was removed just before the break, rounding off a half of frustration for the hosts.
Not wanting to go down without a fight, the Shrimps came out after the restart in determined fashion.
Finding joy through direct play, Andrew Fleming almost grabbed a goal back before the hour-mark when he latched on to a loose ball in the box, but his low drive flashed inches wide of Krysiak’s post.
Encamping themselves in the Yeovil box, Morecambe continued to pile on the pressure and were rewarded in what was to become a frantic final 20 minutes.
An initial Krysiak save only ballooned into the air, bobbling on the Town line for a seeming age before the persistent Oliver headed into the back of the net.
Buoyed by their opener, the hosts continued to press and seven minutes later made it 2-2.
Former Town man Michael Rose swung over a deep cross which found Wigan loanee Lang, whose header back across goal slipped across the line.
Now facing a raucous home crowd, the Green and Whites momentarily silenced the Globe Arena but for the 92 travelling Town fans.
Gray’s corner was whipped in dangerously, allowing Sowunmi to glance a header into the far corner for his second goal in as many games.
In a game full of twists, Morecambe responded immediately and within a minute were providing a moment of deja vu as they levelled for the second time.
The ball spurted into the path of the poaching Lang, who squirmed a shot under Krysiak to make it 3-3 with his second of the night.
Back in the driving seat once again, Bentley’s side produce one more moment of note as Ellison headed home a stoppage-time winner with his fifth goal in six matches against the Glovers, to round off a five-goal second half.
Defeat in Lancashire was Yeovil’s first defeat in five, as 2017 ended in defeat for Way’s side.
Morecambe: Roche; Muller (Kenyon 39’), Old, Lavelle; McGowan, Fleming (Thompson 86′), Rose, Conlan, Lang; Oliver, Ellison.
Bookings: Muller 27′, Ellison 90′, Rose 90′
Subs not used: Nizic, Campbell, Lund, Osborne, Jordan.
Yeovil Town: Krysiak; Mugabi, Sowunmi, N. Smith, James; Gray, C. Smith, Worthington, Khan (Green 73′); Surridge, Zoko (Olomola 70′).
Bookings: N. Smith 63′, Krysiak 79′
Subs not used: Maddison, Davies, Nelson, Santos.