The Hatters were in control after racing into a two-goal lead in the opening stages with goals from Josh Allen and Millar Matthews-Lewis, before the home side pilled on the pressure in the last half-an-hour after Henry Snee headed home.
In a highly-competitive game, Adrian Forbes’ side made the perfect start under the lights at Shefford Sports Club, taking the lead through Allen’s low strike.
Neat combination play between Tyrelle Newton and Conor Lawless created the opportunity, before the striker was able to put the finishing touches on a quick move, with Shefford unable to prevent the ball crossing the line.
Dominating possession, it wasn’t long before the next chance was created and consequently dispatched by Mathews-Lewis. Fresh from scoring a hat-trick for the Under 18s against Southend United U18s on Saturday, the forward was back amongst the goals in the 11th minute, sweeping home Josh Williams’ low cross.
On the other flank, Avan Jones was a well-used outlet in the first period, often free and in space to receive the ball on the right-hand-side. His speed was proving a thorn in Shefford’s defence too, as he was almost a provider but his cross was missed by Allen and everyone else in the penalty area.
Matthews-Lewis had his eyes on a brace and may well have found it, but for a vital sliding challenge from captain Charlie Milton.
The home side then reminded the Development Squad that they weren’t here to make up the numbers in the competition, as Snee was denied by the post one-on-one with Jameson Horlick.
Casey Pettit was the architect for the next chance just after the half-an-hour mark, splitting the defence with a smart pass into Jayden Luker’s feet. The number seven shuffled the ball onto his left foot but Kyle Foster was equal to it, saving well to his right.
Matthews-Lewis had the ball in back of the net a few minutes later but was denied by the offside flag after converting on the goal line, which once again involved a Jones delivery from the right.
Josh Odell-Bature was introduced at the start of the second half in a like-for-like change with Jack Bateson at centre-back.
It was 10 minutes into the half when the next opportunity presented itself to the young Hatters as Luker took aim from the edge of the box but curled his shot over the crossbar.
There was a twist in the tale as the home side pulled a goal back after the hour mark through Snee. After he denied by the post in the first period, he wasn’t to be stopped with a diving header after Metcalfe’s initial shot was saved by Horlick.
Shefford substitute Charlie Thake was booked shortly before Allen’s name was also taken by the referee as the close contest threatened to boil over.
The home side continued to push for an equaliser and so nearly found it on three occasions in the closing stages.
Josh Williams was on hand to clear the ball off the goal-line, before Ben Tompkins headed away a deep cross that looked to be heading for the far corner and Horlick prevented Louie Dillon's low effort.
Under pressure in front of more than 900 supporters, the Under 21s kept their composure to see out the victory on a cold night to book a second round tie against the winner of Biggleswade Town against Biggleswade FC.
Shefford Town & Campton: Foster; Lewis, Cooksley, Milton (C), Lusty (Dillon 86'), Foley, Day (Robinson 85'), Snee (Thake 67'), King, Metcalfe (Ingham 67'), Ansell-Carter
Subs not used: O'Neill.
Goals: Snee (63')
Yellows: Thake (80'), Milton (90')
Luton Town: Horlick; Jones, Bateson (Odell-Bature 46'), Tompkins, Williams; Pettit (C), Luker, Newton; Lawless; Allen, Matthews-Lewis
Subs not used: Moffat, Nicolson, Trialist, Pinnington
Yellows: Allen (81')
Goals: Allen (6'), Matthews-Lewis (11')