After a bright start from both teams the visitors opening the scoring midway through the half when Richie Bennett was perfectly placed to head past a hapless Nathan Baxter.
The unusual attacking threat of Matt Worthington almost drew the scores level but it was the Shrimps who took the lead into the break.
Seeking a first comeback victory since August 2017, two goals in four minutes from Tristan Abrahams set Town on track for an important three points.
Steven Old looked to have ruined the turnaround by equalising but substitute Ryan Seager restored the hosts’ lead in the dying embers of the match with a stunning strike to claim a massive three points in Somerset.
Boosted by injury returns to create something of a selection headache, Darren Way made three changes from the 11 that started last weekend.
Absent since the end of September with ankle ligament damage, Omar Sowunmi took the captain’s armband at the heart of defence, with Tom James returning from suspension to take the left-back spot.
Further forward, Tristan Abrahams was rewarded with a starting spot after coming off the bench seven days ago as his role on the right wing saw Rhys Browne start at right-back for the first time.
With a plethora of players to choose from Carl Dickinson, Jake Gray, Josh Grant and Yoann Arquin missed out on the matchday 18 to sit out the clash along with Gary Warren (hamstring), Sessi D’Almeida (shoulder), Craig Alcock (knee) and Gabby Rogers (calf).
Looking for an early lead, both sides went close to opening the scoring before the 10-minute mark when first Richie Sutton’s header grazed the top of the bar for the visitors, followed by James almost marking his return to the side by curling in a 20-yard strike.
Continuing to be an end-to-end affair Rhys Oates forced Baxter into a quickfire double save which Town quickly responded to by seeing Courtney Duffus drag a shot across the face of goal from the angle.
The opening quarter-of-an-hour saw both sides show plenty of attacking intent and suggested the deadlock was soon to be broken, and so it proved on 22 minutes.
Aaron Collins legwork down the right-hand side led to a teasing cross being stood up to the back post which was perfect for Bennett to head home from close range.
Looking to break an unfortunate record of not being able to come back from behind in 2018/19, the green and whites almost drew level on the half-hour mark.
Alex Fisher’s run to the byline ended with a cross being looped back towards the midfield run of Worthington whose well-hit drive from inside the box was brilliantly palmed away by the outstretched arm of Mark Halstead.
With that chance coming before a lull in proceedings, the rest of the half played out as something of a non-event other than Baxter being forced to tip Jordan Cranston’s free-kick over the bar as a precaution.
Town’s stopper was called into action again immediately after the restart, as Piero Mingoia’s strike came through a number of bodies before resting in the arms of the on-loan goalkeeper.
Flying out of the traps, Jim Bentley’s side registered another attempt on goal soon after but Baxter was again equal to Cranston’s strike from range which took a knick off of Adel Gafaiti on the way through.
Needing to swing the pendulum of momentum in their favour, Way introduced Alex Pattison and Francois Zoko in quick succession as the game ticked towards the hour-mark.
But it was Abrahams who set the game alight with two vital strikes in quick succession.
His first on 58 minutes owed much to the brilliant trickery of Alex Dobre who weaved past a succession of visiting defenders before teeing up Duffus, whose touch fell into the path of the on-loan Norwich striker to emphatically sweep home his first goal for the club.
Back by a now raucous home crowd the turnaround was complete before many had stopped celebrating the equaliser thanks to another cool finish.
Alefe Santos’ run to the byline ended with a ball into Zoko, his shot on the turn ricocheted into the path of Abrahams who then coolly curled into the bottom corner.
Looking like a dream afternoon at Huish Park, the visitors threw a spanner in the works with the game inside the final 10 minutes.
A corner swung into the box was stabbed goalwards by Old and nestled in the back of the net to stun the hosts.
Not to be denied, Yeovil-boy Seager was given a fairytale when his shot and turn from 25 yards spectacularly cannoned in off the bar to cue pandemonium.
With more than 10 minutes of stoppage time played the Glovers had an uneasy closure to the match but clung on to pick up a huge three points in the basement battle in Sky Bet League Two.
Yeovil Town: Baxter; Browne, Sowunmi, Gafaiti, James; Abrahams, Worthington (Pattison 52′), Santos, Dobre; Fisher (Zoko 57′), Duffus (Seager 82′).
Bookings: Santos 42′, Zoko 90′.
Subs not used: Nelson, Mugabi, Ojo, Arnold.
Morecambe: Halstead; Mills, Sutton, Old, Conlan; Mingoia, Kenyon (Mendes 80′), Cranston, Oates (Ellison 69′); Collins, Bennett (Mandeville 69′).
Bookings: Kenyon 46′, Sutton 57′, Cranston 90′, Ellison 90′, Halstead 90′.
Subs not used: Roche, Hedley, Dalby, McKay.