Town took the lead early in the contest as Avan Jones smashed in a penalty, but they were pegged back in the 35th minute as Alex Bonnington fired home from 15-yards out.
Toby Kenyon put the Owls ahead on the stroke of half-time before Wednesday quickly added a third after the re-start as Bonnington scored once more.
Coree Wilson scored a second for the Hatters in the 61st minute and despite having a few chances to equalise, Town couldn’t find another goal.
Under-18 lead coach Dan Walder made two changes for tonight’s fixture after losing to Oxford United in the EFL Youth Alliance Cup last week, with goalkeeper Jameson Horlick and right-back Jones both brought into the starting line-up.
The game started with action at both ends – right-back and captain for Wednesday Lewis Farmer hit the bar from a deep cross in the second minute but from there, the Hatters took control of the opening exchanges.
Tra Lucas produced a lovely flick-on towards Wilson, who ran through on goal and was brought down by Farmer for a penalty kick.
Jones took the resulting penalty and fired the ball into the top corner to put Town 1-0 up in the tenth minute.
Wednesday threatened not long after with a free-kick from the edge of the box and on the rebound, L’Varn Brandy hit a hard, driven shot towards goal which was well held by Jameson Horlick.
The away side created another reasonable chance as the ball found its way to Charles Hagan in the box, but the winger fired over the bar.
Wednesday's continued pressure paid off in the 35th minute when they equalised through Bonnington. The forward burst through and fired a left-footed effort across goal and into the far corner.
The Owls took the lead on the stroke of half-time as Kenyon headed in Farmer’s corner kick and three minutes after the re-start, extended their lead as Bonnington scored his second of the evening.
From a corner delivery the ball wasn’t cleared and dropped kindly to the striker – who stabbed the ball into the bottom corner.
Bonnington had a chance to grab his hat-trick in the 55th minute as he raced through on goal but as he cut back onto his right foot and produced a goal-bound effort, Joe Halsey got back in time to make a good block on the line.
The Hatters then got themselves back in the game with some good build-up play which Wilson capped off. The forward tapped the ball into an empty net just after the hour mark after Jackson originally saved from Lucas but he was there to score at the second attempt.
Just a few minutes later, Wilson had another good chance after stretching to get on the end of Nicholson’s cross into the box but was flagged offside in the process.
Substitute Ed McJannet was brought down in the box in added time after receiving the ball from Coree Wilson but the referee waved away shouts for a penalty.
Wednesday progressed quickly down the other end of the pitch and Bonnington again had a chance to score his hat-trick – but was denied well by Horlick.
Despite late pressure, the Hatters couldn’t find an equaliser and exited in the third round of the competition.
TOWN: Horlick, Halsey, Jones (McJannett 45), Wedd, Francis (Kalonda 83), Beckwith (C), Pettit (Allen 87), Nicolson, Newton, Lucas, Wilson. Subs not used: Swan, Boorn, Stevens, Corbit
Goals: Jones (10), Wilson (61)
Yellows: Pettit, Halsey
SHEFFIELD WEDNESDAY: Jackson, Farmer, Ellery, Kenyon, Thompson, Cox, Hagan, Glover, Bonnington, Hall (Reaney 90), Brandy (Aguas 71). Subs not used: Hare, Curtis, Oliver, Trueman, Zottos
Goals: Bonnington (35, 48), Kenyon (45)
Yellows: Farmer, Bonnington, Hagan, Aguas
Attendance: 281
