The Town's survival bid took a huge blow as results elsewhere combined with their sixth home defeat of the season leaves them 16 points from safety with 12 games left.
Exeter surged into a two goal lead with goals from Adam Stansfield and Liam Sercombe before a Tom Craddock goal six minutes before the break gave the Hatters hope.
The Hatters huffed and puffed and twice hit the woodwork. Chris Martin and Sam Parkin both saw efforts come off the goal frame but the Grecians shut up shop and the Town couldn't find away through the visitors defence.
A win for Grimsby and a draw for Bournemouth leaves the Hatters 15 points adrift at the bottom and 16 away from safety.
Hatters manager Mick Harford was true to his word following his Friday press conference and kept the faith with the same 11 that drew with Gillingham on Tuesday night.
That meant new loan signing goalkeeper David Button had to make do with a place on the Town's substitutes' bench. That was the only change to the manager's bench
Exeter had their own Spurs loanee in their ranks with the grandly-named Troy Archibald-Henville lining up to form a three-man central defensive trio.
With a very healthy contingent of Grecians packed in the Oak Road, Exeter kicked off sporting their all blue away strip, chasing a seventh win on the road.
It didn't take long for those Exeter fans to have something to celebrate when on four minutes when they took lead.
Adam Sercombe floated a cross from the right and striker Adam Stansfield was left free to nod home from six yards past Dean Brill.
The Grecians were enjoying a good spell with their quick, slick football impressing going forward.
But the Hatters responded well. On six minutes Tom Craddock had a shot deflected into the hands of Exeter goalkeeper Paul Jones and on nine minutes Chris Martin cut inside from the left and blasted a right-foot shot against the top of the crossbar.
On 12 minutes Asa Hall found Ian Henderson with a terrific ball inside the Exeter left channel and after cutting inside Rob Edwards the former Northampton man warmed the gloves of Jones.
Four minutes later, after Archibald-Henville was booked for a foul on Martin down the Town left, Henderson's free-kick found Craddock at the far post but his header was held by Jones.
The Town continued to press and Jones had to be alert to tip away an in-swinging Henderson corner and then moments later Martin shot wide of the goalkeeper's right-hand post.
Martin had another chance on 27 minutes calling Jones into action with a left-foot shot from a tight angle after being found by Craddock.
Exeter had rarely threatened since opening the scoring but that all changed two minutes when Sercombe turned from provider to goalscorer to double the visitors' lead.
Alex Russell's right-wing cross was tipped away by Brill preventing Stansfield from tapping home but the ball ran kindly for Sercombe who was free at the back post to fire high into the net.
The Grecians nearly added a third a minute later when Mark Bower had to be quick to clear the danger after Stansfield had got the better of Keith Keane and squared the ball across goal.
Effervescent Marcus Stewart, had up until now been anonymous in the proceedings for the visitors, but on 32 minutes he combined with Dean Moxey which saw the former Ipswich striker hit the side netting.
Then four minutes later the 36-year-old saw a header flash past Brill's left-hand post following Moxey's corner.
However, the Hatters got an important goal back six minutes before the break to reduce arrears.
Kevin Gallen sent Henderson scampering down the right flank and after beating his marker, he squared for Craddock who fired through a sea bodies past Jones for his seventh goal of the season.
The one-goal deficit could and should have been extended 30 seconds later when Steve Basham beat the Town's offside trap and only had Brill to beat.
However, inexplicably the striker decided to shoot first time with time on his side straight into the relieved arms of Brill.
With the Hatters' confidence boosted by the goal, they almost got an equaliser on 39 minutes but again were denied by the woodwork for the second time in the match.
Ed-Asafu-Adjaye launched a searching cross deep from the right flank which found Parkin lurking at the back post but after beating his marker in the air the striker saw his header bounce agonisingly off the crossbar.
HALF TIME: LUTON TOWN 1-2 EXETER CITY
The Hatters began the second period in search of an early equaliser but despite enjoying plenty of possession the nearest they came in the opening 10 minutes of the half a shot from Craddock that curled over the bar.
On 64 minutes Harford made his first change of the afternoon when introducing Ryan Charles for Henderson.
Neither side had forced a save from either goalkeeper until Basham had a close range effort saved by Brill on 66 minutes after good work down the Exeter right by Stansfield.
The Hatters continued to press but could just not find away past the visitors.
With six minutes left as the Town searched in vain for an equaliser, Harford made a double change bringing on Jake Howells and Michael Spillane for Gallen and Martin.
As time ticked away Parkin played a one-two with Keane but as Exeter defenders converged on the Town skipper he could only poke his shot narrowly wide of Jones's right-hand post.
In the 90th minute a right-wing cross from Spillane was headed just wide of the target from Charles but that was the closest the Town came and Exeter held on for all three points.
FULL TIME: LUTON TOWN 1-2 EXETER CITY
Luton Town: Brill, Davis, Keane, Henderson (Charles 64), Parkin, Hall, Asafu-Adjaye, Martin (Howells 84), Bower, Craddock, Gallen (Spillane 84).
Substitutes not used: Gnakpa, Button.
Booked: Bower (88)
Exeter City: Jones, Gill, Taylor, Stansfield (McAllister 83), Basham (Cozic 74), Edwards, Moxey, Sercombe (Saunders 60), Archibald-Henville, Russell.
Substitutes: Marriott, Seaborne.
Booked: Archibald-Henville (16)
Referee: C. Boyeson
Attendance: 6,460 (including 748 from Exeter).
Sponsors Man of the Match, chosen by Hartwell Ford: Kevin Gallen.
