The Bees first chance fell to John Akinde, but he saw his effort save by Christy Pym. Soon after, Jack Taylor fired across the face of goal as Barnet looked the more dangerous of the two sides in the opening minutes.
Exeter broke the deadlock just after the half hour mark. Jayden Stockley won the ball before Wilson curled a left-footed shot into the bottom corner from the edge of the box, leaving Ross helpless in the Barnet goal.
Shaquile Coulthirst had an effort cleared off the line by Jordan Moore-Taylor, Exeter then went up the other end, but Matt Jay was denied by a fine save by Craig Ross.
Ryan Watson drew Barnet level and sent the travelling 124 members of the Bee Army into raptures in the 70th minute with a simply stunning free-kick into the top corner from 20 yards out.
Jamal Campbell-Ryce was unlucky to see his cross come back off the crossbar, but in stoppage time Jake Taylor let fly just inside the penalty area and found the bottom corner.
Barnet FC – Ross, Clough, Santos, Watson, Akinde (Nicholls 85′), Campbell-Ryce, Coulthirst, J. Taylor, Fonguck (Akinola 60′), Vilhete, Blackman.
Unused: R. McKenzie-Lyle, Brindley, Nelson, Tutonda, Sweeney.
Watch Mark McGhee’s post match interview below.