Pressure is mounting on Chris Turner as his Wednesday side failed to halt a run of seven league games without a win.
The promotion favourites are now sliding slowly towards the relegation zone after squandering chances.
Turner even threw on French trialist Mickael Antione-Curier with 10 minutes to go playing with four strikers in an attempt to break down Luton's stubborn defence.
Wednesday stretched the Luton defence in the 18th minute after winning a corner on the right. Defender Brian Barry-Murphy picked out Robbie Mustoe who turned quickly to lash in a low shot smothered by the driving Marlon Beresford.
Former Wolves striker Adam Proudlock tried his luck with a shot from 20 yards minutes later, stopped on the line by the Luton keeper.
Wednesday should have snatched the lead in the 22nd minute, Leigh Bromby 's long throw found Lloyd Owusu who flicked the ball onto Michael Reddy, but from six yards he pulled the ball wide.
The Sheffield side escaped minutes later, Luton striker Adrian Forbes whipping in a stinging shot from long range, smothered at the second attempt by Kevin Pressman.
Owusu threw away an opportunity firing straight at Beresford from 15 yards, before Luton caught Wednesday on the break, leading scorer Steve Howard firing narrowly wide from 25 yards before Pressman pulled off a fingertip save to keep out the lively Forbes.
Defender Graeme Lee almost broke the deadlock in the 67th minute stretching to meet a Barry-Murphy corner, only for former Wednesday keeper Beresford to snatch his close-range header.
Wednesday squandered another chance 10 minutes from time as Reddy burst into the area, but the ex-Sunderland man chose to shoot from a tight angle, with Owusu unmarked, and Beresford saved at the near post.
Antoine-Curier was handed a half-chance in the dying minutes after a scramble in the Luton goalmouth, his low strike cut out by Beresford.