Having not conceded a goal in their last four league outings, Town conceded two in the first-half at the Lamex Stadium.
Luke Amos’ 25-yard strike put the hosts ahead, before Jonathan Smith doubled Stevenage’s lead in additional time with another shot from outside the box.
Needing a big second half performance Town got off to a nightmare start, as Danny Newton rifled home a third Boro goal just a minute after the restart.
Ben Kennedy added a fourth on 58 minutes to put the result beyond doubt, making Ryan Seager’s first goal for his hometown club little more than a consolation.
Darren Way made two changes from Tuesday night’s win over Barnet, as Otis Khan returned from a five-match suspension to replace Jordan Green (ill), whilst Alefe Santos came in for Oscar Gobern (rested).
Top scorer Francois Zoko missed out on a return to his former club due to suspension, earning Connor Smith a recall to the bench.
Looking to avoid a first ever EFL defeat to Boro, the Glovers started on the front foot looking to carry on where they left off in midweek.
Tom James’ long throws proved to be an early threat, causing chaos in the hosts’ box with Omar Sowunmi at the centre of the action.
However, Darren Sarll’s side began to warm up after a slow start and registered the first shot of the game when Mark McKee’s looped ball into the box was volleyed wide by Danny Newton.
If Newton’s strike was a warning, it wasn’t acknowledged by the visitors who conceded their first goal in six hours of league action with 16 minutes on the clock.
Neat build-up freed up space for Amos 25 yards out, whose dipping effort nestled in the bottom corner past a hapless Jonny Maddison.
With the home crowd in full voice, Boro remained on the front foot after taking the lead and almost doubled their advantage 10 minutes later.
Opening up in the box, Maddison raced from his line to stand big and block McKee’s powerful strike from close range to keep it at 1-0.
After Stevenage engineered some early momentum, the Green & Whites swung the pendulum in their favour midway through the half with two chances in quick succession.
Strong running from Jake Gray saw the winger burst into the box only for Ben Wilmot to produce a last-ditch block, before James fired a long-range free-kick into the side-netting minutes later.
Becoming an even encounter, Yeovil were dealt a blow on the stroke of half-time as Stevenage made it 2-0 in similar fashion to the first.
Unleashing from 20 yards, Smith picked out the opposite corner to midfield partner Amos to give Town a mountain to climb after the break.
But matters got worse for Way’s side almost instantly.
Clearly buoyed by their ending to the first-half, Stevenage flew out of the traps and made it 3-0 on 46 minutes when Kennedy’s inch-perfect cross was side-footed home by Newton.
An instant response was needed from Way’s side if there was to be anything to be taken away from the Lamex Stadium, but Surridge’s half-volley at the back post was well kept out by Tom King to increase the visitors’ frustrations.
However, if the game wasn’t already put to bed it was before the hour-mark when the Hertfordshire outfit added a fourth.
A Boro corner never left the final third and falling to Kennedy in the box, Stevenage’s number 10 worked the ball into space before drilling home from the angle.
Continuing to battle, the Green & Whites still searched for a way back into the match and were almost given a glimmer of hope when Lewis Wing’s strike from the edge of the box was tipped over the bar by King.
Penning Stevenage back, Town were rewarded for their refusal to give up when Seager poked home his first goal for the club following a mistake in the box from substitute Kevin Lokko.
The closing stages could have been different had Surridge not headed over the bar from a few yards out just moments later, as Boro survived to batten down the hatches and see out a first ever EFL win over Yeovil.
Stevenage: T. King; Vancooten, Wilmot, King, Martin (Lokko 74′); Amos, Smith, McKee, Goddard; Kennedy (Bowditch 80′), Newton (White 90′).
Bookings: Martin 36′
Subs not used: Fryer, Franks, Wilkinson, Conlon.
Yeovil Town: Maddison; Whelan, Sowunmi, James, Dickson; Gray, Santos (Browne 46′), Wing, Khan (Gobern 52′); Fisher (Seager 64′), Surridge.
Bookings: Khan 42′, Wing 82′
Subs not used: Phillips, Donnellan, Bird, C. Smith.