Logan collided with Tommy Rowe as he tried to reach Jabo Ibehre's cross, but could only punch the ball into his own net.
Stockport opened purposefully and put pressure on the Saddlers' defence in the early stages.
After six minutes Chris O'Grady flicked the ball beautifully into Oli Johnson's path, but the youngster looked on in disbelief as his super shot from 18 yards bounced back out off the post.
Within a minute O'Grady fired a powerful shot straight at visiting keeper Rene Gilmartin.
However, despite the hosts' impressive start, Walsall took the lead after 12 minutes. Sofiene Zaaboub's corner-kick wasn't cleared, and there was centre-back Anthony Gerrard, who fired home the loose ball from 12 yards in at the near post.
Five minutes later Zaaboub swung in another excellent cross, but Troy Deeney headed over the crossbar from a great position.
On 27 minutes O'Grady found space in the Walsall box again, but this time his snapshot was well saved by Gilmartin.
Just past the half-hour mark teenage centre-back Josh Thompson came to Stockport's rescue when he was on hand to clear Deeney's goalbound shot to safety with 'keeper Logan stranded.
At the other end Johnson neatly played Matty Mainwaring, only for the energetic midfielder to scoop a shot disappointingly into the sidenetting from close range.
There was a lively start to the second half with Zaaboub forcing Logan into a good save at one end and Peter Thompson smashing a volley just wide at the other.
On 61 minutes the hosts fluffed the best chance of all. Ibehre inexplicably lifted a hand to Greg Tansey's cross in the Walsall box, and a penalty was awarded.
However, Rowe stepped up and promptly skied the penalty kick high over the crossbar.
Stockport did level on 76 minutes though. Sub Danny Pilkington was tripped just outside the box, and up stepped Tansey to curl the free-kick round the wall and in at the near post.