James Collins scored the only goal of the game midway through the first half after he missed a penalty in the first minute of the match.
The result marks the second clean sheet Town have kept in the league this season, lifting them off the foot of the table and to within seven points of safety.
Graeme Jones made one change to the starting line-up following defeat against Cardiff City on Saturday, with captain Sonny Bradley returning in place of Cameron Carter-Vickers. Danny Hylton started amongst the substitutes, involved in the matchday squad for the first time since March last year.
The game kicked-off in the most remarkable fashion as the Hatters were awarded a penalty after 15 seconds. Izzy Brown played the ball through to Pelly Ruddock-Mpanzu, who was dragged to the ground and referee Gavin Ward pointed to the spot. Collins stepped up but smashed his effort off the bar.
After Wednesday regrouped and produced attacks of their own, Ryan Tunnicliffe had an effort on goal which Cameron Dawson did well to hold. Dan Potts switched play from the left which Tunnicliffe dummied and left for James Bree, who produced a low ball in towards the midfielder, which he caught on the half-volley but it was rebuffed by the goalkeeper.
Town continued to make chances and in the 18th minute, Mpanzu whipped a ball into the box for Collins, who chested down towards Brown, but he skewed his left-footed effort just wide of the post.
After missing a penalty in the early stages, Collins made amends by scoring the opening goal in the 23rd minute. Cornick caught the Owls at the back, rounded Dawson and squared the ball back to Collins, who fired into an unguarded net.
The striker had another presentable chance fall his way just after scoring his 10th goal of the season, but as Mpanzu’s miss-hit shot fell to him, he could only fire over the bar.
Simon Sluga produced a fine save to deny substitute Kadeem Harris on the hour mark, who struck well from outside the area.
Wednesday were pushing for an equaliser and came very close to getting it just a few minutes later. Harris this time turned provider and teed up defender Julian Borner, but from close range he could only head wide.
In the closing stages Town had the ball in the back of the net once more as Brown’s corner was lashed in by Potts, though a foul on Dawson before he fired home meant the goal was ruled out and celebrations were cut short.
The Hatters endured a nervy five minutes of added time but held on to gain a valuable three points with a game against Middlesbrough next up on Saturday.
TOWN: Sluga, Bree, Pearson, Bradley (C), Potts, Tunnicliffe, Rea, Mpanzu, Brown (Shinnie 90), Cornick (Hylton 68), Collins. Subs not used: Shea, McManaman, Carter-Vickers, Moncur, LuaLua.
Goals: Collins (23)
Yellows: Brown, Bree, Rea
SHEFFIELD WEDNESDAY: Dawson, Iorfa, Lees (C), Borner, Palmer (Murphy 71), Lee, Bannan, Da Cruz, Windass (Nuhiu 61), Forestieri (Harris 45), Wickham. Subs not used: Wildsmith, Pelupessy, Hunt, Urhoghide.
Yellows: Wickham
Referee: Gavin Ward
Attendance: 10,001 (1,018 away)
