Giles Coke, who was later sent off along with Millwall's Shane Lowry for fighting, had given the Owls the lead halfway through the second half but Campbell headed home an 80th-minute equaliser after Liam Feeney's effort came back off the post.
An elaborate Steve Morison flick in the third minute found Andy Keogh in space but after he then slipped in Lee Martin, the winger just could not get his shot away.
Chris Kirkland was then called into action for the first time on 10 minutes, saving comfortably first from Danny Shittu's weak header and then denying Morison from an acute angle.
A misplaced pass-back by Wednesday's Oguchi Onyewu, under pressure from Ryan Fredericks, let Martin in again two minutes later but Kirkland spread himself well to save with his legs.
Atdhe Nuhiu had Wednesday's best chance of the first half just before the half-hour when Jeremy Helan picked him out unmarked on the six-yard line but he failed to hit the target with his header.
Just 30 seconds into the second half and Millwall were nearly ahead but Kirkland was at full stretch to deny Morison's looping header that was destined for the top corner.
At the other end Stephen Bywater almost saw substitute Caolan Lavery's tame cross crawl into the net after he let the ball slip through his hands but he recovered to palm the ball away from Nuhiu.
Campbell was introduced for his Lions debut on 56 minutes and 10 minutes later sent Morison clear on the right and when he squared to Liam Feeney only he will know how he missed from six yards.
Then, against the run of play two minutes later, Coke made an excellent run to bisect the Millwall defence and rounded Bywater to score into an empty net for an unlikely lead.
Miguel Llera then saw his header deflected onto the bar as the visitors searched for a second goal but it was Millwall who drew level threw Campbell.
Referee Lee Probert allowed play to continue with Morison down clutched his head in the Wednesday six-yard box but after Feeney had hit the post from Fredericks' cross, Campbell slotted home the equaliser.
Tempers flared late on as Lowry and Coke were both shown red for a scrap by the corner flag which saw both sets of players rush in to separate the pair.
With eight minutes of added time Millwall looked the more likely to score but after Kirkland blocked another Campbell effort with his chest well out of his area neither side could find a winner.