Sam Surridge grabbed a brace for the Glovers either side of Olufela Olomola’s 27th-minute strike, before the latter saw red for his association with an on-field tussle.
Substitute Kevin Toner was also dismissed for his part in the incident, and Francois Zoko was later sent off for a high foot as Darren Way’s side hung on for victory with nine men.
The Yeovil manager made three changes from his last league outing, including fourth Sky Bet League Two starts for AFC Bournemouth loanees Surridge and Matt Worthington.
Versatile Welshman Tom James was utilised at left-back in place of concussed Ryan Dickson.
There was also a first involvement in the matchday squad for Academy goalkeeper Tommy Scott, who was named on the bench after an injury to Jonny Maddison in training.
The hosts lined up in a very attacking shape and Olomola twice stretched the visitors’ defence early on, first seeing his cross narrowly evade fellow forward Zoko before a further move fizzled out.
Stevenage looked vulnerable at the back but after Dale Gorman’s volley deflected over, they created the first clearcut chance.
Omar Sowunmi’s clearance cannoned off Worthington, fell kindly for Chris Whelpdale who swivelled and hit the foot of the post.
A flurry of offsides followed alongside a wild Tom Pett volley as a lull in the match ensued.
It was sparked back into life by a great finish from Surridge.
After a fierce James Bailey strike appeared to hit Fraser Franks’ hand in the box, the young striker kept his composure to send a side-footed effort into the bottom corner.
Moments later it was two with all four forward players contributing.
Surridge flicked on to Zoko who in turn nudged the ball on to Otis Khan. He raced through and found himself in a two-on-one situation with Olomola, unselfishly squared to the Southampton youngster who tucked away with aplomb.
The Glovers were rampant and passing the ball round superbly, deservedly adding a third of the afternoon before the break.
Khan proved the provider once more, whipping a lovely corner to the back post where Surridge was waiting unmarked to smash home his second of the day.
It was almost a dream first period for the 19-year-old, who got in a great position to receive Zoko’s slide-rule pass only for his heavy touch to deny him his hat-trick opportunity.
Then a long Artur Krysiak punt somehow reached Zoko but he could merely find the legs of keeper Joe Fryer rather than Yeovil’s fourth of the day.
Boro almost reduced the deficit early in the second half and it would have been helping hand from a Green and White shirt.
Whelpdale’s diagonal ball was collected by Dan Newton whose shot from an acute angle was tipped out by Krysiak, inadvertently hit Nathan Smith and just dropped wide of the post.
Former Tamworth man Newton was denied by Town’s number one again prior to the hour mark. He weaved in and out of number of players before being thwarted by the legs of Krysiak.
Similarly to the first half, chances went quiet and then all hell broke loose.
A mass brawl occurred right in front of the touchline and following a five-minute consultation with his officials, referee Chris Sarginson showed red cards to Olomola and substitute Toner for their part in the fracas.
Back to pitch action and when the storm had calmed, Khan warmed the gloves of Fryer with a curling effort and Tom James’ knuckleball free kick forced the away stopper into a flying save.
Yeovil ended the contest with nine players when Zoko received a red card for a raised foot but it didn’t effect the final result as the home side recorded back-to-back league wins in Somerset.
Yeovil Town: Krysiak, Mugabi, Sowunmi, N.Smith, James, Bailey, Worthington, Khan (Browne 82), Surridge, Olomola, Zoko.
Bookings: Bailey 42.
Sending off: Olomola 63, Zoko 82.
Not used: Scott, Davies, Nelson, C.Smith, Gray, Santos.
Stevenage: Fryer, Henry, Vancooten (Wilkinson 46), Franks (Toner 54), Martin, Whelpdale, King, Gorman, Pett, Newton, Wootton (Samuel 46).
Bookings: King 28, Martin 63, Gorman 88.
Sending off: Toner 65.
Not used: Day, Conlon, Slater, Wilmot.