In a free-flowing encounter, Town took the lead just before the half-hour mark courtesy of Matty Dolan’s expert free-kick, whilst keeping Alexandra contained at the other end.
As the first-half ticked into additional time Jean-Louis Akpa Akpro made it 2-0 with a deft header, before the game was put beyond any doubt after the break.
With 20 minutes remaining Otis Khan netted from close range to round off an impressive Town performance, virtually ensuring the Glovers league status and making any real relegation fears short-lived.
Darren Way made two changes to the side that came away empty handed from the Good Friday trip to Newport County.
The experienced head of Alex Lawless came into the centre of a midfield four in place of Matt Butcher, whilst Jean-Louis Akpa Akpro replaced Omar Sowunmi upfront.
On the bench, the Glovers continued without a substitute goalkeeper, with Jonny Maddison making his home league debut in place of the injured Artur Krysiak.
After an assured start from the visitors who were quick to settle on the ball, the Glovers grew into the match and began to trouble the Railwaymen.
Francois Zoko’s first-time shot into the arms of Ben Garratt was the game’s first attempt on goal, whilst Alexandra failed to trouble Maddison despite working themselves into dangerous positions in the final third.
In fact, it took David Artell’s side until almost the half-hour mark to cause the Yeovil stopper any issues, as Callum Cooke’s shot deflected causing Maddison to scramble to beat the lively Chris Dagnall to the ball.
That warning from Crewe sparked Town into life, who took the lead with 29 minutes on the clock as Dolan marked his 100th appearance in style.
Having won a free-kick 25 yards from goal, Khan laid the ball off for Dolan who picked out the top corner with a stunning curling effort, in a similar strike to the one that won the reverse fixture in Cheshire back in October.
Having reeled off to celebrate with manager Way and with the home support in a more buoyant mood, the Railwaymen were continually frustrated by the offside flag to deny Dagnall a charge through on goal.
In an open and expansive encounter at Huish Park, Crewe had their best chance when Callum Ainley’s shot from the edge of the box ricocheted into the arms of a thankful Maddison, before the hosts doubled their lead.
Clever work from captain Ryan Dickson won the Glovers a free-kick in first-half stoppage time, and from Khan’s pinpoint delivery wide on the left, Akpa Akpro rose highest to open his Yeovil account and end the opening 45 minutes on a high.
With their League Two status already virtually assured, Crewe made two attacking changes at the break as they threw caution the wind in search of a way back into the match.
Immediately from the restart Alexandra got numbers in the box and forced Town to be on their metal defensively, but martialled by an imperious Nathan Smith, the Glovers stood firm with Maddison remaining untroubled.
As the game ticked towards the final 20 minutes Yeovil looked to put their Cheshire counterparts to the sword and looked to have done so when Akpa Akpro bundled in a third, but his effort was ruled out for deliberate handball.
The Glovers weren’t to be denied for long, however, as with 70 minutes on the clock Khan marked his home return after almost three months out through injury with a goal, following up Zoko’s header which cannoned back off the bar.
Akpa Akpro forced Garratt into a smart save from the angle as Yeovil brimmed with confidence and searched for a fourth, but Way’s side had to settle for 3-0 and a result which put real distance between the Glovers and the bottom two with only three games remaining.
Yeovil Town: Maddison; Shephard, Lacey, Smith, Dickson; Dawson, Lawless, Dolan, Khan; Akpa Akpro, Zoko.
Bookings: Zoko 24’, Akpa Akpro 65’
Subs not used: Mugabi, James, Butcher, Goodship, Harrison, Eaves, Sowunmi.
Crewe Alexandra: Garratt; Turton, Ray (Wintle 45’), Ng, Bakayogo; Jones, Cooke (Kiwomya 45’), Bingham; Bowery, Dagnall, Ainley (Cooper 59’).
Bookings: Cooper 81’
Subs not used: Dawber, Saunders, Udoh, Kirk.