The midfielder popped up at the death to volley Steve Flack's flick past Steven Drench to deny Morecambe victory.
It was a goal that left the home side and supporters devastated after they had come from behind with a rousing second-half display.
Billy Jones had given Exeter the lead ten minutes into the second half with a penalty awarded after Michael Twiss had harshly been adjudged to have handled Jones' right-wing corner.
But it was a goal the game badly needed after an edgy first half which saw neither side manage to find top gear.
After a poor first hour the game became an end-to-end thriller with Morecambe stepping up the pace after Gary Sawyer had gone close to putting the visitors 2-0 up on 67 minutes.
Garry Thompson's pace down the right was an integral part of the Morecambe revival but it was new signing Stuart Barlow who sparked the Shrimps into life with a debut goal on 68 minutes with a neat finish after Chris Todd's slip.
Barlow came close again moments later when he forced Jones into a neat save at his near post from Thompson's cross before the Shrimps made it 2-1 on 75 minutes.
Thompson was again the provider with a superb low cross which fizzed across the six-yard box until Ged Brannan slid in to steer the ball home from close range.
The Shrimps continued to press with Thompson forcing Jones into another neat save after a superb piece of skill ten minutes from time.
But then with 91 minutes on the clock Challinor scored perhaps his most important goal of the season as he latched on to Flack's flick to poke the ball past Drench from close range.
The first half was something of a drab affair with neither side failing to get anywhere near top gear.
It was Challinor who had the best chance of the half when, on 18 minutes, he made space for himself on the edge of the box and curled a shot that was heading for the bottom left-hand corner until Drench made a fine save.
Morecambe's best opening came in first half injury-time as Danny Carlton's corner was met by the late arrival of Bentley at the far post but his header was off target.