There were few chances in a scrappy first half, but Lennell John-Lewis brought the game to life when he put his side ahead early in the second half. Lincoln controlled the game after the break and could have won comfortably.
But in the closing stages substitute Craig McAllister levelled with a header and deep into injury time before Moxey grabbed a winner with a close-range strike.
There were precious few goal-scoring opportunities at either end during a scrappy opening half.
Lincoln offered little as an attacking force although John-Lewis struck a shot just past the post on the half-hour mark.
Five minutes before the break Lee Frecklington thumped a volley over the bar from the edge of the box. Paul Green then had a shot deflected wide as the visitors ended the half strongly.
After the break Lincoln's David Graham tested Paul Jones with a shot from the edge of the box but the Exeter goalkeeper was equal to the effort.
The visitors were ahead six minutes after the restart. Graham's shot was parried by Jones and when Moxey cleared the ball off the line John-Lewis was in the right place to tap the ball into an empty net.
The striker should have made it two ten minutes later when he met Dan N'Guessan's cross but struck the ball against the post from close range.
Daniel Hone went close for Lincoln when he headed over from 12 yards. Jones then denied N'Guessan as the visitors looked to increase the lead.
But Exeter pulled level against the run of play in the 74th minute when McAllister met Matt Gill's long throw and nodded the ball home.
With two minutes left N'Guessan was sent off for a professional foul on Moxey and in injury time McAllister flicked on a long ball and Moxey thumped the ball into the bottom corner.