Town's biggest crowd of the season - 9,500 - was treated to a feast of attacking football from both sides that saw goals from Kenwyne Jones for the Owls and Steve Howard for the Hatters either side of half-time.
An unrelenting pace from start to finish saw the Hatters force ten corners and hit ten shots on target, but in-form Wednesday also looked dangerous on the break.
Both sides pushed forward in a frenetic start to the game, before Rowan Vine pulled back from the right for Kevin Nicholls to curl an 18-yard shot straight at David Lucas.
Marlon Beresford held Paul Heckingbottom's 24-yard free-kick at the second attempt in the 23rd minute, but Luton continued their ferocious pace and Chris Coyne saw a thumping header from Steve Robinson's corner tipped over by Lucas three minutes later.
Kevin Foley was the next to try his luck when he beat two defenders on the corner of the penalty area and cut inside to fire a low left-footed shot at Lucas from 16 yards in the 36th minute.
Wednesday responded with a left-foot bullet from their own right-back Lee Bullen that flew just wide from 20 yards in the 41st minute.
Robinson's 44th minute ball into the box caused mayhem as Howard and Vine both came close to converting, but the Owls took the lead out of the blue on the stroke of half-time.
Beresford and Curtis Davies left a long ball to each other and Jones was given the simple task of poking home into the empty net for the softest of goals.
Luton responded in style just 33 seconds after the interval when Robinson's thunderbolt from the edge of the area bounced back off the stanchion and Ahmet Brkovic nodded on for Howard to head home from six yards.
The end-to-end nature of the game continued when Matt Hamshaw broke down the right in the 53rd minute and crossed for Steve MacLean to head at goal from eight yards - only for Beresford to save to his right.
Glen Whelan shot just wide from another Hamshaw cross a minute later before Howard tested Lucas with a 25-yard snapshot that was pushed around the post.
Joey O'Brien then volleyed wide from ten yards after he was presented with a glorious chance by John Paul McGovern in the 63rd minute and Vine streaked clear a minute later and turned inside to shoot at Lucas from 16 yards.
Vine then missed a chance to seal the win when he ran clear on to Paul Underwood's pass with eight minutes remaining only for Lucas to block his shot.