Bullen was forced to go between the sticks when goalkeeper David Lucas was stretchered off just before half-time.
But it was referee Steve Tanner who incensed the home fans with a nightmare 63rd minute.
Millwall forced a corner and David Livermore saw his effort fly straight in. But the referee saw a foul on Bullen and awarded a free-kick to the visitors.
And while the Millwall players were celebrating what they thought was a goal Wednesday went up the other end and scored.
It was seven Owls players against three Millwall defenders and it ended with Frankie Simek volleying in his first goal for the club.
The angry Millwall players surrounded the referee but despite the protests the goal stood.
The Lions then pushed on but could not find a way past the stand-in keeper as the visitors came away with an unlikely win.
In an even first half Millwall midfielder Marvin Elliott went close early on before home keeper Andy Marshall had to be quick off his line to deny Barry Corr on 25 minutes.
The turning point of the game came on 37 minutes when Matt Lawrence's hopeful ball into the Wednesday box saw Elliott challenge Lucas, who went down in a heap clutching his leg.
The Owls keeper tried to carry on but barely lasted five minutes, as it was clearly visible that he couldn't continue. And with no keeper on the bench captain Bullen took over between the sticks.
On the hour mark Wednesday were lucky to still have 11 men when Richard Wood pulled down Berry Powel on the edge of the box when the Dutch striker was clean through.
The referee had a different outlook to the foul to the home fans and only showed Wood a yellow card.
From the resulting free-kick Livermore curled a delightful chip over the wall, only for Bullen to pull off a fantastic fingertip save.
And it was from that corner that Wednesday broke to score the winner.