With fellow title chasers Grays Athletic beaten 2-1 at home to Accrington Stanley, Alex Inglethorpe's team didn't waste the opportunity to return to the summit.
But the Grecians had to settle for a point after Altrincham, rarely in the contest, sprung a late shock when leading scorer Colin Little snatched an equaliser.
A wonderful pass from Colin Potts set the striker through on goal, and he duly fired into the top right-hand corner with a fierce left-foot drive on the run.
Earlier, high-flying Exeter started the better of the two sides and after nine minutes found the net from a Craig Farrell header only for the effort to be ruled out for offside.
Altrincham were always second best in the tackle, and in the 26th minute Andy Taylor saw a bending free-kick well saved by Stuart Coburn.
But five minutes later Exeter broke the deadlock when former Manchester City midfielder Tony Scully crossed from the right and Challinor, unmarked at the back post, headed past Coburn and into the left-hand corner. Scully could have made it 2-0, but fired over the bar from distance.
Altrincham failed to make a clear-cut chance on goal in the first half, and it was not surprising that Exeter always looked the most likely to add to Challinor's opener.
Left-back Billy Jones saw a free-kick fly into the side netting, and on the stroke of half- time Scully saw a shot, from the tightest of angles, land on the roof of the net.
The second half saw Lee Phillips pick out Farrell with a pin-point cross, but he saw his point-blank shot brilliantly saved by Coburn.
At the other end Altrincham saw substitute Stephen Rose cross for Little, who headed over, but six minutes later Little grabbed a point for his side after a quick counter attack left Exeter on their heels, but it was not enough to stop them from going top of the table.