Story of the match
It was the struggling visitors who started on the front foot, with former Hatter Izzy Brown blasting over, after Luton struggled to deal with Callum Paterson's long throw into the area.
Sheffield Wednesday opened the scoring a minute later, when Josh Windass tapped home from Paterson's cross.
The Yorkshire club continued their early dominance in the opening 20 minutes as they prevented the hosts from even breaking out of their own half.
The pace and energy of Windass caused a number of problems early on and he could have made it two in the 22nd minute when he latched onto Barry Bannan's through ball, but the forward's effort narrowly blazed over.
Windass did manage to make it two just 20 minutes later, converting with a thunderous strike, after the Hatters failed to clear a cross from the edge of the box.
After a below par first half from the home side, Nathan Jones opted to make a triple substitution in a bid to change the dynamic of the game.
A decision that certainly woke them up and the Hatters halved the deficit just four minutes into the second half, when Kal Naismith flicked home Kiernan Dewsbury-Hall's scoffed corner kick.
Seven minutes later and the Town were level with Ryan Tunnicliffe scoring just his second goal in a Luton shirt, slotting past Joe Wildsmith after brilliant work from Elijash Adebayo.
In the 85th minute, Adebayo scored his second goal in as many games, nodding home Harry Cornick's deep cross into the box.
The Hatters nearly had a fourth in the fifth minute of injury time when Harry Cornick got beyond Chey Dunkley, but his pull-back was just about cleared before Adebayo could tap in.
Sheffield Wednesday looked devastating in attack in the first half. They recorded 12 shots compared to Luton's one and they really could have been out of sight. The Hatters responded brilliantly to their first half disappointment and spent the majority of the second as the better side.
The visitors now sit six points off Birmingham City in 21st place with their chances of survival diminishing.
Elijah Adebayo put in another good performance for his new club, setting up Luton's second goal, scoring the third and causing the Sheffield Wednesday backline chaos in the second half.
Josh Windass was a constant threat in the first half. He made the most of the makeshift Luton defence and scored both Wednesday's goals. He could have scored a couple more in a 45 minutes that Wednesday completely dominated.