Caolan Lavery gave the home the lead four minutes before the break, but the Yorkshire club could not hold on to claim the three points.
Charlton were the ones to have the first shot on target; a tame effort from Gudmundsson that was all too easy for Keiren Westwood.
Charlton kicked on and arguably had the better chances of the first 20 minutes, including a contentious disallowed goal from Chris Eagles who looked to be at least two yards onside when the ball was played to him.
Wednesday responded with a quick counter-attack, despite the state of the Hillsborough pitch, but they could not finish the job as their four-on-three surge ended with a weak shot from Lewis McGugan finding the arms of Stephen Henderson.
The best opportunity of the half fell to Charlton. After a scramble in the penalty area, Igor Vetokele laid the ball off to Simon Church but with only the goalkeeper to beat, from three yards Church struck his shot straight at the legs of Westwood.
And it was Wednesday who took the lead just before the break. A cross from out wide by Lewis Buxton found Lavery who volleyed past Henderson from close range.
The second half started off a lot slower than the first. In fact it took 18 minutes for the first chance to present itself. Lavery was the provider this time, crossing in from the wing, but Chris Maguire’s chance at a clear cut chance was cut out by the head of Roger Johnson in the Charlton defence.
Charlton had threatened to score throughout the game so it came as no surprise when they finally levelled the scores with 15 minutes left to play. A half-hearted parry from Westwood fell to Gudmundsson and he was able to fire the ball into the net.
Wednesday looked to respond straight away and twice hit the bar in the space of a minute. First a long range effort from Lavery and then an overhead kick from the troublesome Lloyd Isgrove.
With the final whistle approaching it appeared that the Owls had created the chance to claim all three points. Buxton made another run down the wing and provided a sublime ball for an unmarked Atdhe Nuhiu to head into an empty net, but somehow the big centre forward failed to hit the target.