Having had the better first-half chances in an edgy encounter, Town broke the deadlock just before the break courtesy of a clinical Jean-Louis Akpa Akpro finish.
The Glovers were worthy of their lead at the halfway mark but were pegged back on 53 minutes, courtesy of Josh McQuoid’s poachers finish.
Both sides had chances to win it, but Stevenage’s hopes of a top seven finish were to be dealt a blow in Somerset as Yeovil quashed any fears of relegation with a game to spare.
Darren Way gave the starting XI that disappointingly lost at Grimsby a week ago a chance to make amends, making no alterations within the 18-man matchday squad.
That meant the Green and Whites continued without the services of Kevin Dawson (leg) and Artur Krysiak (ankle), with Darren Ward ruled out for the remainder of the season back in March.
With both sides targeting three points for different reasons, it was a positive start to proceedings in Somerset with plenty of attacking intent – albeit without much fruition.
Looking to make the unlikely event of relegation mathematically impossible, the Glovers were first to go close to opening the scoring, with Matty Dolan’s strike from range slamming into the side netting inside 10 minutes.
The positive start continued for Town when the lively Otis Khan cut inside from the left, before watching a curling effort drift just wide.
That was as good as it got in terms of goal scoring opportunities inside the opening half an hour, as it became a cagey affair at Huish Park, with Jonny Maddison comfortably dealing with tame efforts from Tom Pett and Ben Kennedy.
The potential consequences of defeat for both sides saw defensive solidity take priority, before Way’s side ended the opening 45 minutes on a high.
After a spell of pressure saw the hosts entrench themselves in the Boro half, Akpa Akpro made it 1-0 after 44 minutes.
Good work and tenacity from Khan on the left saw a ball swung into the box, and the Barnet loanee was perfectly placed to expertly dispatch a first-time effort into the net for his second in three matches.
Keen to secure their EFL status in style Yeovil ended the half with a succession of attacking corners, only for the referee’s half-time whistle to offer Darren Sarll’s side some respite.
With results elsewhere hampering Stevenage’s play-off hopes the visitors needed to find an equaliser, and did so just eight minutes after the restart.
A swift counter-attack won Boro a corner, and from the resultant set-piece McQuoid was picked out with a header back across goal to level the scores.
If the goal was against the run of play it sparked a good spell for the Hertfordshire outfit, as Maddison had to be at his best to push a fierce Steve Schumacher shot around the post.
The young stopper was called into action again before the hour mark to palm away Jobi McAnuff’s rasping strike from inside the box, before Town almost restored their lead as the game became an end-to-end affair.
Good work from Akpa Akpro saw him beat Jack King before reaching the by-line, with his pullback being pushed just wide by Francois Zoko, under pressure from Dean Wells in the middle.
As the chances continued to flow, Tom Pett enjoyed two in quick succession for Boro, seeing a well-hit effort stopped by Maddison before heading into the side netting moments later with 73 minutes on the clock.
Chasing a second goal to keep their play-off spot, Stevenage made all three substitutions and threw centre-back Jack King upfront, as Yeovil looked to earn the point that would ensure their EFL safety.
On course to do so, Maddison demonstrated his shot-stopping ability once again to brilliantly keep out Jamie Gray’s low strike, as the game ticked into the final few minutes.
Keen to not drop points on the road, Sarll’s side threw numbers forward in the closing stages but couldn’t trouble Man of the Match Maddison further, meaning Town earned the point needed to retain their EFL status.
Yeovil Town: Maddison; Shephard, Lacey, Smith, Dickson; Whitfield (Butcher 90’), Lawless, Dolan, Khan; Akpa Akpro, Zoko.
Subs not used: Mugabi, James, Goodship, Harrison, Eaves, Sowunmi.
Stevenage: Jones; Henry, Wells, King, Ogilvie; Lee (Gray 74’); Kennedy (Tonge 68’), Schumacher, Pett, McAnuff; McQuoid (Wilkinson 81’).
Subs not used: Franks, Day, Gorman, Ntlhe.