Miracle worker Chris Turner needs a win at Brighton on Monday for his Wednesday side to have a chance of avoiding the drop.
Wednesday, with two successive victories behind the, including a 2-1 win at promoted Portsmouth last week carved out few opportunities in a scrappy game against fellow strugglers Grimsby.
Shefki Kuqi was handed a half chance in the opening minutes, Lloyd Owusu threading the ball to the big striker who charged through unmarked before drilling a low shot straight at the diving Danny Coyne.
Michael Reddy lashed the ball into the side netting from a Richard Evans corner as Wednesday looked for an opener before two saves by keeper Kevin Pressman kept Grimsby out.
Full back Tony Gallimore was foiled in the 24th minute, his curling free kick evaded the wall as the ball crashed against the unsighted keeper before he managed to hack it away.
Panicky Wednesday cleared straight to the lurking Chris Bolder who produced an eye catching strike from 25 yards tipped round the angle by the veteran Wednesday keeper.
Midfielder Alan Quinn pulled a low strike wide of the target before Wednesday escaped a sending off. A mistake by Danny Maddix let in Michael Boulding and centre back Dean Smith had no option to upend the Grimsby striker.
Referee Phil Dowd was lenient showing Smith a yellow card before Stuart Campbell pulled his free kick over the top.
Boulding went close with a wicked deflection curling narrowly wide of the far post and Richard Hughes was inches away in the 75th minute as he met a Michael Keane corner to finish with a twisting header.
Substitute Steve Haslam headed over as the Owls side piled players forward in the dying minutes in a last ditch attempt so snatch the points.