After a bright start the hosts took the lead just past the 10-minute mark when Jordan Cook capitalised on a ricochet to pick out the bottom corner from the edge of the box.
After ending the first half the stronger the Glovers were embroiled in a six-goal second half thriller, which started with Alan Sheehan’s free kick from range.
The visitors responded just eight minutes later through Francois Zoko, before Isaac Vassell immediately restored the Hatters two-goal advantage.
With 65 minutes on the clock substitute Omar Sowunmi rose high to head home at the back post, but Luton took just 60 seconds to make it 4-2 through the potent Danny Hylton.
The action continued but Luton rounded off the scoring in stoppage time as Vassell neatly slotted home a second, to end the visitors cup run.
Darren Way made four changes to the side that came away from Hartlepool United with a share of the spoils in Sky Bet League Two at the weekend.
Without eight first team players, Yeovil fielded only four substitutes at Kenilworth Road.
Bevis Mugabi came in for the suspended Liam Shephard whilst Kevin Dawson – able to play in the Trophy despite a ban in the league – replaced former Luton favourite Alex Lacey (knee).
Spurs loanee Shayon Harrison made his first Glovers start in place of the cup-tied Jean-Louis Akpa Akpro, with Jonny Maddison continuing his run in the competition between the sticks.
With a home semi-final tie awaiting the winner, the Hatters looked to make the most of their quarter-final home advantage with an impressive start to the game.
Maddison had to be alert from the get-go to smother Jonathan Smith’s drilled cross before racing from his line to beat the lively Danny Hylton to the ball moments later.
Harrison, making his full senior debut, stung the fingertips of Matt Macey at the other end before a combination of Mugabi and Nathan Smith managed to thwart Isaac Vassell when baring down on the visiting goal.
The young stopper had to be on hand again inside the opening 10 minutes to dive low to his left to push away Pelly-Ruddock Mpanzu’s low shot, before Luton finally found a way past Maddison.
A ricocheted cross fell kindly to the feet of Cook on the edge of the box, who made no mistake picking out the bottom corner.
Nathan Jones’ side continued to threaten in the final third looking to capitalise on a re-shuffled Yeovil back four, but Town slowly came into the game.
Matty Dolan saw a shot from range tipped over by Macey before good feet from Harrison engineered space to shoot inside the box, with the Hatters ‘keeper forced into a diving save.
Keen to build themselves a safety barrier, Smith saw a rasping drive from 18 yards cannon back off the bar against the run of play, leaving the woodwork shaking for some time.
With an eventual Wembley final in the horizon the Glovers finished the half the stronger as Dolan saw another effort flash inches wide, as Way’s outfit began to influence proceedings at a sparsely populated Kenilworth Road.
Despite encouragement before the break, Town were dealt a blow just six minutes after the restart courtesy of a Sheehan set-piece.
After Butcher felled Vassell 25 yards from goal, the free kick specialist brilliantly picked out the top corner with Maddison not able to keep the effort out.
That triggered a goal frenzy with five goals in 16 second-half minutes, as Zoko latched on to Sowunmi’s flick-on to neatly slot past Macey with 58 minutes on the clock.
Seemingly back in the game Yeovil conspired to return momentum to the hosts when Vassell’s solo run ended with a powerful finish past Maddison after cutting in from the left just 180 seconds later.
Before the home crowd had returned to their seats it was 3-2 when Sowunmi rose at the back post to expertly loop a header back where it came from over Macey, as Yeovil looked to trigger a comeback once again.
Any danger of that was soon ended – just 60 seconds later, when Hylton slammed Vassell’s low cross home off the crossbar.
That was the last of the goal frenzy but the action continued.
Dolan saw a dipping free-kick drop just wide, before Maddison denied Hylton on two occasions with smart saves.
As the game entered the closing stages Luton rounded off the scoring through Vassell in stoppage time, rounding off a disappointing night defensively for Town.
Luton Town: Macey; O’Donnell, Mullins, Senior; Rea, Mpanzu, Smith, Cook (Cuthbert 63’); Vassell (Marriott 90’), Hylton (Justin 90’).
Bookings: Rea 57’, Senior 67’
Subs not used: King, Gray, Lee, Gambin.
Yeovil Town: Maddison; Mugabi, Butcher, Smith Dickson (James 78’); Whitfield (Goodship 81’), Dawson, Dolan; Harrison, Eaves (Sowunmi 53’), Zoko.
Bookings: Dawson 30’, Sowunmi 86’
Subs not used: Krysiak.