Neither side could find a breakthrough in the opening 45 minutes at The Shay, but Curtis Weston fired the visitors ahead in the 67th minute.
Martin Allen's men looked to have secured the three points despite seeing David Stephens dismissed for a second bookable offence, but Maynard netted in the dying seconds to earn the home side a point.
Ben Strevens fired the home side ahead from the penalty spot in the 17th minute, but Louis Moult brought Wrexham level. Neil Ashton struck again in the first half for the visitors who looked to be heading for the three points, only for Constable to net late on to save the hosts.
The result leaves Telford 15 points adrift of safety with just seven games left in the campaign. Meanwhile, Gary Mills's men are six points off the playoff places with two games in hand on sixth-placed Forest Green.
Alfreton Town earned a vital point in their quest for survival in their match against Lincoln City as they played out a goalless draw at North Street, which moved Nicky Law's men four points clear of the drop zone.
Sparkes fired the visitors ahead in the fourth minute, but John Campbell brought Torquay level. However, Sparkes added goals either side of the break, while Matt Paine and Ryan Peters notched late strikes to secure a comfortable victory.
Deverdics opened the scoring in the 11th minute and the home side held the lead until Gianluca Havern equalised 11 minutes from time. However, Deverdics netted his second of the game in the dying minutes to earn his side the win.
Results in full: AFC Telford 0-1 Gateshead, Alfreton Town 0-0 Lincoln City, Chester 1-2 Dartford, Dover Athletic 2-1 Altrincham, Eastleigh 2-2 Wrexham, Halifax 1-1 Barnet, Torquay United 1-5 Braintree Town