Jay Tabb had given the visitors a bizarre lead at the break, but Wednesday rallied to earn a point from the match.
Town nearly doubled their lead just three minutes later, but Luke Hyam's volley was saved by Kirkland.
The home side made two separate substitutions midway through the first half. First Kieran Lee was the victim of a tactical swap as he was replaced by Steve Howard, before injury forced Johnson to be swapped for Chris Maguire.
After the break it was the away side who had the first chance of the half, but Guirane N'Daw's 20-yard volley flew just wide.
However, Wednesday found an equaliser on the hour mark when Maguire and Lewis Buxton partnered up on the right before finding Lita at the back post to blast home.
The Owls nearly went in front just three minutes later, but Miguel Llera glanced his header wide from six yards.
Wednesday cleared a goalbound effort off the line for the second time in the match when Pugh acrobatically erased the danger.