The Owls were held to a frustrating draw which set a frustrating evening for the Owls as they dominated most of the game.
And despite having almost all of the possession throughout, the hosts had to settle for a share of the spoils.
Following a quiet start, Wednesday found their stride ten minutes in and might have taken the lead but for the unfortunate positioning of Fernando Forestieri six yards from goal.
Sam Winnall clipped a Wallace cross goalwards but the ball ricocheted off Forestieri and back into play.
The Argentine striker then turned poacher, trying his luck from 20 yards but Jon McLaughlin was down swiftly to save.
Wallace this time chanced his arm from distance and saw his daisycutter fly past McLaughlin and nestle in off the post.
The goal, though, saw Burton free the shackles and after Keiren Westwood twice denied Marvin Sordell, the visitors hauled themselves back into the game on 24 minutes.
A corner was headed clear but only as far as Irvine on the edge of the area and the Australian smashed an unstoppable volley home with the aid of the post.
Play went straight back the way of Wednesday and Bannan fired narrowly wide before Forestieri almost caught out McLaughlin with a cross that the keeper just managed to pluck from beneath the crossbar.
Across a packed backline, Forestieri forced a good save from McLaughlin as Wednesday asked all the questions.
Substitute Adam Reach brought another fine stop from McLaughlin and the keeper was then alert to thwart Jordan Rhodes.
A string of corners followed, one of which landed with Forestieri, who fashioned an overhead kick that fell the wrong side of the post.
Rhodes was inches away from a Bannan teaser and the closing stages saw complete dominance from the hosts, but Burton held firm to extend their run of resistance to five games in their battle for survival.
Sheffield Wednesday Head Coach Carlos Carvalhal said : “It’s a game that is very easy to explain. One team that came to achieve one point – which I understand – and another team that tried to win since the beginning.
“Of course I am not happy with the score, but I am happy with my players. Why? Because to play against a team that puts ten players in front of the area is not easy and I think we did what we must do.
“Most of the time we achieved good positions in the wide areas to cross and we did a lot of crosses with quality, but we didn’t put the ball inside the net.”
Burton manager Nigel Clough said: “It was backs-to-the-wall at times and I thought we defended magnificently, to a man.
“We tried to be a threat but it’s very difficult against quality opposition like Sheffield Wednesday. You can’t play open, expansive football.
“We had to work hard and the only disappointment was the goal we conceded, but we got back on equal terms quickly. If we are to survive, it’s got to be a scrap and a battle and you could see the determination to succeed.”
Man of the Match – David Jones: Best performance in a Wednesday shirt so far for Jones and read the game well.
Wednesday: Westwood, Hunt, Sasso, Loovens, Fox (Buckley 80), Wallace (Reach 52), Bannan, Jones, Forestieri, Winnall (Fletcher 67), Rhodes
Subs: Wildsmith, Fletcher, Reach, Palmer, Semedo, Buckley, Nuhiu
Subs: Bywater, Mousinho, Woodrow, Murphy, Palmer, McCrory, Miller